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THE  NEW 

Elementary  Arithmetic 


BY 

JOHN  W.  COOK 

PRESIDENT    ILLINOIS    STATE    NORMAL   UNIVERSITY 
AND 

MISS  N.  CROPSEY 

ASSISTANT    SUPERINTENDENT    CITY    SCHOOLS 
INDIANAPOLIS,    INDIANA 


SILVER,    BURDETT    &   COMPANY 

New  York  . . .  BOSTON  .  .  .  Chicago 

1899 


C7 


Copyright,  1893,  1895,  1899, 
Br    Silver,  Burdett  and  Compan? 

EDUCATION  DEPtfi* 


SUGGESTIONS. 


IT  has  been  said  that  the  " new  education  "  proceeds  to  give  the 
child  an  experience,  instead  of  presupposing  one  for  him. 
Pupils  become  practical,  not  by  learning  forms  of  reasoning,  but 
by  exercising  the  reason  upon  their  own  plane  of  comprehension. 

In  such  a  spirit  this  Elementary  Arithmetic  has  been  pre- 
pared. It  presents  three  years'  work,  based  upon  carefully  graded 
exercises,  which  may  be  used  as  a  means  of  training  pupils  to 
think,  and  of  teaching  at  the  same  time  the  practical  application 
of  numbers  to  ordinary  business  transactions. 

The  first  and  hardest  step  in  solving  an  arithmetical  question  is 
to  determine  the  processes  required ;  the  second,  to  state  the  dif 
ferent  steps  of  the  solution  in  proper  arithmetical  form. 

It  is  very  important  that  children  should  master  the  fundamental 
processes  so  thoroughly  that  they  come  to  serve  thought  without 
loss  of  time  or  energy.  The  patient  following  of  these  graded  ex- 
ercises and  drills  should  secure  this  result.  The  tables  of  "  End- 
ings," in  addition  (see  pages  58,  61,  etc.),  have  the  same  practical 
use  as  the  multiplication  table,  and  should  be  as  thoroughly 
applied. 

Each  chapter  presents,  in  general,  division  and  multiplication  as 
converse  processes,  followed  by  subtraction  and  addition  on  the 
same  general  plan.  In  the  beginning  each  number  is  viewed  as  a 
whole,  divisible  into  equal  parts,  and  the  parts  are  viewed  in  rela- 
tion to  the  whole  and  to  each  other. 

No  formula  should  be  taught  with  the  thought  that  it  will  do 
the  thinking  for  the  pupil.  Let  the  problem  be  pictured,  and  this 
followed  by  the  expression  in  figures,  before  any  formal  expression 
in  words  is  attempted.  Give  a  very  thorough  drill,  as  on  page  13, 
Article  2,  before  pupils  are  required  to  find  these  relations  in  con- 
crete problems. 

The  object  of  picturing  problems  is  not  to  teach  children  to 
make  pictures  (though  all  this  work  should  be  done  with  reason- 
able  care),  but  to  give  a  method  of  representation  by  which  they 

54 1 52' 


4  SUGGESTIONS. 

can  make  their  thoughts  clear  to  themselves.  It  is  a  means,  not 
an  end,  and  should  be  so  regarded.  When  problems  can  be  stated 
clearly  and  solved  correctly  there  is  no  further  necessity  for  picture 
representation,  except  as  a  means  of  testing  the  pupil's  comprehen- 
sion of  spoken  or  written  forms.  Let  not  objective  work  be  un- 
derrated, however.  It  is  a  very  necessary  means,  which,  rightly 
used,  will  secure  an  accurate  knowledge  and  use  of  terms,  and  save 
much  time  and  confusion  later  on.  Pupils  should  learn  early  to 
show  objectively  the  difference  between  six  and  one-sixth  of  six. 
between  one-sixth  of  six  and  one-sixth  of  one,  etc. 

Two-step  and  three-step  problems,  which  may  be  worked  out 
orally  in  the  recitation,  will  often  be  found  too  difficult  for  a 
written  test.  The  indiscriminate  use  of  "miscellaneous  prob- 
lems" may  do  much  harm. 

All  measures  introduced  should  be  learned  by  actual  use  (see 
page  65).  The  standards  in  common  use,  such  as  the  yard,  foot, 
ounce,  pound,  quart,  etc.,  can  be  obtained  easily,  and  should  form 
a  part  of  the  regular  school  supplies.  Exercises  in  estimating 
volume  and  extension  train  the  judgment  while  giving  practical 
results  in  knowledge,  and  there  is  no  time  in  the  course  when 
pupils  can  better  afford  to  do  this  work. 

Having  worked  Part  I.  to  learn  what  and  how,  a  profitable  re- 
view can  be  made,  directing  chief  attention  to  why.  Rules  should 
be  made  by  the  pupils  after  the  process  is  learned  from  which  the 
rule  is  derived. 

Long  Division  is  one  of  the  difficult  processes  for  children.  At 
first  they  are  unable  to  judge  how  many  times  the  divisor  is  con- 
tained in  the  dividend  or  partial  dividend.  When  about  to  com- 
mence Long  Division  much  mental  practice  should  be  given  with 
small  numbers,  13,  14,  15,  16,  etc.,  —  such  drill  as  13  in  14,  13  in 
15,  13  in  16,  etc.,  to  13  in  117;  same  drill  with  14,  15,  16,  etc. 

For  additional  suggestions,  see  "New  Advanced  Arithmetic," 
page  51. 

This  book  has  grown  from  experience,  and  is  offered  to  fellow- 
teachers  as  a  thoroughly  systematic  work-book, 

N.  C. 

Indianapolis,  January,  1899. 


PEEFACE. 


IT  has  seemed  to  the  authors  of  the  Normal  Course 
in  Number  that  there  is  room  for  another  series  of 
Arithmetics,  notwithstanding  the  fact  that  there  are  many- 
admirable  books  on  the  subject  already  in  the  field. 

The  Elementary  Arithmetic  is  the  result  of  the  ex- 
perience of  a  supervisor  of  primary  schools  in  a  leading 
American  city.  Finding  it  quite  impossible  to  secure 
satisfactory  results  by  the  use  of  such  elementary  arith- 
metics as  were  available,  she  began  the  experiment  of 
supplying  supplementary  material.  An  effort  was  made 
to  prepare  problems  that  should  be  in  the  highest  degree 
practical,  that  should  develop  the  subject  systematically, 
and  that  should  appeal  constantly  to  the  child's  ability  to 
think.  The  accumulations  of  several  years  have  been  care- 
fully re-examined,  re-arranged,  and  supplemented,  and  are 
now  presented  to  the  public  for  its  candid  consideration. 

Not  the  least  valuable  feature  of  this  book  is  the  care- 
ful gradation  of  the  examples,  securing  thereby  a  natural 
and  logical  development  of  number  work.  No  space  is 
occupied  with  the  presentation  of  theory,  —  that  side  of 
the  subject  being  left  to  the  succeeding  book.  The  first 
thoughts  are  what  and  how, — these  so  presented  that  the 
processes  shall  be  easily  comprehended  and  mastered. 
Subsequently,  the  why  may  be  intelligently  considered  and 
readily  understood. 


CONTENTS. 


PART   I. 

Chapter  Paou 

I.    Review  of  Number  Representation  to  30     .    .    .  7-12 
II.   Numbers  from  20  to  30.  —  Partition,  Division,  and 
Multiplication;   Subtraction  and  Addition. — 

Oral  and  Written  Exercises 13-64 

III.  Numbers  from  30  to  40  (treatment  same  as  in  Chap.  II.)  65-99 

IV.  Numbers  from  40  to  50  (treatment  same  as  in  Chap.  II.)  100-122 
V.   Numbers  from  50  to  70  (treatment  same  as  in  Chap.  II.)  123-144 

VI.   Numbers  from  70  to  100  (treatment  same  as  in  Chap.  II.)  145-160 

PART    II. 

I.   Reading  and  Writing  Numbers 161-172 

II.    United  States  Money.  —  Drills  and  Reviews  .     .  173-198 

III.  Notation  and  Numeration.  —  Long  Division.  —  Di- 

vision and  Multiplication.  —  Cancellation  .     .  199-229 

IV.  Common  Fractions 230-249 

V.   Decimal  Fractions 250-266 

VI.    Compound  Numbers 267-287 

VII.   Percentage.  —  Interest 288-297 

VIII.    Miscellaneous  Problems 298-308 


PART  I. 

CHAPTEK    I. 

NUMBERS    FROM   TWENTY   TO    THIRTY. 

1.    Representing  numbers  by  figures. 


are        One  Ten 


mi  nil  n  U    u  U    n  II 


il  ill  till  1 


Place  your  bundles  of  counters  upon  your  slates, 
or  make  drawings  of  these  bundles  of  sticks,  and 


g  ELEMENTARY  ARITHMETIC. 

write  under  each  the  figure  which  stands  for  the 
^ii?,aiid:tljce  figure  which  stands  for  ones. 

2.  Read  the  number  which  you  have  written 
under  each  group. 

In  the  first  group  (one  ten  and  one  one)  the 
figures  are  alike ;  do  they  mean  the  same  thing  ? 

What  does  the  figure  on   the   left   represent  ? 

Which  is  more,  one  one  or  one  ten? 

Which  is  of  more  value,  a  one-cent  piece  or  a 
ten-cent  piece  ? 

How  many  ones  make  one  ten  ? 

One. one  is  what  part  of  one  ten? 

3.  Begin  with  1,  and  write  in  a  column  the 
figures  which  stand  for  the  numbers,  through 
nineteen. 

To  the  left  of  each  write  the  word  which  stands 
for  the  number. 

In  the  number  ten,  which  figure  stands  for  no 
ones  ? 

Words :     naught,  one,  two,  three,  four,  five,  six,  seven,  eight,  nine. 
Figures:       0  1234567         8        9 


One  Ten           One  Ten  and  One 

One  Ten  and  Two 

One  Ten  and  Three 

10 

11 

12 

13 

Ten              Eleven 

Twelve 

Thirteen 

One  Ten  and  Four 

One  Ten  and  Five 

One  Ten  and  Six 

14 

15 

16 

Fourteen 

Fifteen 

Sixteen 

One  Ten  and  Seven 

One  Ten  and  Eight 

One  Ten  and  Nine 

17 

18 

19 

Seventeen 

Eighteen 

Nineteen 

NUMBERS  FROM   TWENTY   TO    THIRTY.  9 

4.  One  ten  and  two  ones  are  how  many  ones  ? 
Twelve  ones  are  how  many  tens  and  ones  ? 
Eighteen  ones  are  how  many  tens  and  ones  ? 
16  ones  are  how  many  tens  and  ones  ? 

1  ten  and  8  ones  are  how  many  ones  ? 

5.  Add  one  more  to  your  nineteen  sticks.    How 
many  tens  have  you? 

J  J  Two  Ten* 

How  many  ones  besides  the  two  tens  ?       &>  a 

Untie    the    bundles;    how  many   ones      >tl=j| 

have  you  ?  ■  ™ 

J  Twenty 

Tie  the  two  tens  tightly  together,  place 
them  on  your  slate,  and  write  under  this  bundle 
the  figure  which  stands  for  the  two  tens.     To  the 
right  of  the  2  place  the  figure  which  shows  that 
there  are  no  ones.     Read  the  number  (^o*7). 

Two  tens  and  no  ones  are  twenty  ones. 

Read  the  number  you  have  written,  first  as  tens 
and  ones. 

Untie  your  bundles.     How  many  ones  ? 

Read  the  whole  number  of  ones. 

6.  Take  one  more  stick,  and  you  have  how 

many  tens  and  ones  ? 

Write  the  figure  which  stands  for  the       s     J 

I     i 
two  tens;  the  figure  which  stands  for      "     ° 

the  one  one.  JIB 

Untie   the   bundles  of   sticks.      How    (I  II  I 

i  o  Twenty-one 

many  ones  have  you  : 


10  ELEMENTARY  ARITHMETIC. 

Two  tens  and  one  one  are  twenty-one. 

7.  Read  the  number  which  you  have  written. 

Take  one  more  counter ;  how  many 
h     ©      tens  and  ones  have  you  ? 

Write  the  figure  which  stands  for 
the  tens ;  the  figure  which  stands  for 
the  ones. 

Two  tens  and   two  are  twenty-two. 
Write  the  figures  for  this  number. 

Write  the  figures  for  two  tens  and 
three  ones. 

Jill  1 1  Write  the  figures  for  two  tens  and 

||  II     four  ones. 

nun  nil  hiiiiiii 
mini   m 

8.  Draw  these  groups  of  tens  and  ones,  and 
write  under  each  group  the  figures  which  stand 
for  tens  and  ones. 

Two  tens  and  five  ones  are  how  many  ones  ? 
Two  tens  and  six  ones  are  how  many  ones  ? 
Two  tens  and  eight  ones  ? 


NUMBERS  FROM  TWENTY  TO   THIRTY.         \\ 

Two  tens  and  nine  ones  ? 

9.  Take    one   more   counter;    add    it    to    the 
twenty-nine.      How   many    tens    have    you  ? 
Have  you  any  ones  besides  the  three 

«/  *J  Three  Ten* 

tens? 

Tie  your  three  tens  tightly  together. 
Write  the  figures  which  stand  for  three 
tens  and  no  ones. 

Untie  all  the  bundles.  How  many  ones  have 
you  ? 

Three  tens  are  how  many  ones  ?  Thirty  ones 
are  how  many  tens  ? 

10.  Read  these  numbers:  20,  21,  22,  23,  24, 

25,  26,  27,  28,  29,  30.  Write  them  on  your  slate 
in  a  vertical  column.  To  the  left  of  each  write 
the  word  which  stands  for  the  number. 

In  which  line  do  you  find  all  the  ones  ?  In 
which  line  are  the  tens  ? 

29  ones  are  how  many  tens  and  ones  ?  2  tens 
and  6  ones  are  how  many  ones  ?  Which  is  the 
greater,  2  tens  or  2  ones  ? 

11.  The  Roman  letters,  I,  V,  and  X,  are  also 
used  to  represent  numbers.  I  stands  for  one, 
V  for  five,  and  X  for  ten. 

Words :     naught,  one,  two,  three,  four,  five,  six,  seven,  eight,  nine. 
Figures:        0  1234567         8         9 

Letters :  I      II      III      IV     V    VI    VII    VIII      IX 


12  ELEMENTARY  ARITHMETIC. 

Ten     Eleven  Twelve     Thirteen     Fourteen     Fifteen     Sixteen 

10         11  12              13               14              15  16 

X         XI  XII           XIII            XIV           XV          XVI 

Seventeen  Eighteen        Nineteen          Twenty  Twenty-one 

17  18                   19                  20  21 

XVII  XVIII              XIX                XX  XXI 

Twenty-two    Twenty-three  Twenty-four     Twenty-five  Twenty-six 

22  23                    24                    25  26 

XXII  XXIII             XXIV              XXV  XXVI 

Twenty-seven  Twenty-eight            Twenty-nine  Thirty 

27  28                             29  30 

XXVII  XXVIII                     XXIX  XXX 


The  Roman  characters  are  not  now  employed  in 
number  work,  but  are  chiefly  used  for  numbering 
chapters  and  lessons,  and  occasionally  for  number- 
ing some  of  the  first  pages  in  books,  and  in  num- 
bering appendixes  and  indexes.  They  are  also 
used  to  indicate  the  different  volumes  of  a  series 
of  books,  and  to  mark  the  hours  on  the  dials  of 
clocks  and  watches. 

These  uses  give  variety,  and  sometimes  prevent 
confusion.  Since  you  will  meet  these  characters 
in  nearly  every  book  you  take  up,  it  is  well  that 
you  should  know  what  they  mean. 


NUMBERS  FROM  TWENTY  TO   THIRTY.         13 


CHAPTER  II. 

1.  Separate  21  cubes  into  three  equal  groups. 

0000000*  0000000  0000000 

21  cubes  are  how  many  seven-cubes  ? 
3  seven-cubes  are  how  many  cubes  ? 
21  is  how  many  7's  ?     21  =  3  sevens. 
21-r-7  =  3  (21  contains   7  three  times,  or  21 
contains  3  sevens). 

3  sevens  are  how  many  ?     3  sevens  =  21. 
3  times  7  are  how  many  ?     3x7  =  21. 
7  is  what  part  of  21  ?     1  of  21  =  ? 
3  thirds  of  21  are  how  many  ? 
How  many  7's  can  you  take  out  of  21  ? 
Begin  with  21  and  subtract  7's. 
Begin  with  7  and  count  21  by  7's. 
21-7-7-7  =  ?     7  +  7  +  7  =  ? 

2.  Copy  the  following  forms,  and  place  together 
those  which  have  the  same  meaning. 

Which  show  I  of   21  ?     Which   show  that  21 
contains  7  three  times  ? 

21  cubes  -4-  7  cubes  =  3.      21  oranges  ~-  3  =  7  oranges. 

21  cubes  -j-  3  =  7  cubes.      21  oranges  -r-  7  oranges  =  3. 

7  cubes  )  21  cubes.  3  )  21  cubes  to  be  divided. 

3,  number  of  7-cubes  7  cubes, 

in  21  cubes 


14  ELEMENTARY  ARITHMETIC. 

21  miles  -f-  3  =  7  miles.  21  miles  -i-  7  miles  =  3. 

21  yards  -r3  =  7  yards.  21  yards  -r-  7  yards  =  3. 

3 )  21  miles  to  be  divided.     7  miles  )  21  miles. 

7  miles.  3,  number  of  7-miles 

in  21  miles. 

3.  Helen  has  21  nuts  which  she  wishes  to 
share  equally  with  two  playmates.  How  many 
nuts  will  each  receive  ? 

Into  how  many  equal  groups  must  the  nuts  be 
divided  ?  There  are  three  children,  so  the  nuts 
must  be  divided  into  three  equal  groups. 

We  count  off  one  to  each  child  in  turn,  until  we 
have  used  all  the  nuts. 

000000000000000000000 

First  child,  ©  ©  ©  ©  ©  ©  © 
Second  child,  ©©©©©©© 
Third  child,      ©©©©©©© 

Each  child  will  get  I  of  21  nuts,  which  is  7  nuts. 

Slate  work :         3  )  21  nuts,  to  be  divided. 

7  nuts,  each  one  receives. 

Divide  21  sheets  of  paper  equally  among  3  pu- 
pils. How  many  sheets  will  each  pupil  receive  ? 
What  part  of  the  paper  will  each  get?  (Make 
picture.) 

Make  a  problem  for  this  form :  J  of  21  =  7. 


NUMBERS  FROM  TWENTY  TO   THIRTY.         15 

4.  I  have  21  cents  to  spend  for  Christmas  cards ; 
if  I  pay  7  cents  apiece,  how  many  can  I  buy  ? 

ooooooo  ooooooo  ooooooo 
D  D  D 

I  can  buy  1  card  for  7  cents.  I  can  buy  as  many  cards 
for  21  cents  as  there  are  7-cents  in  21  cents. 

There  are  three  7-cents  in  21  cents.  21  cents  will  buy 
3  cards  at  7  cents  each. 

Slate  work :     7  cents )  21  cents. 

3  (7-cents  in  21  cents). 
21  cents  will  buy  3  cards  at  7  cents  each. 

At  7  cents  each,  how  many  cakes  can  George 
get  for  21  cents  ?  (Make  a  picture  for  this  prob- 
lem.    Express  in  figures.) 

Note  to  the  Teacher.  The  picture  language  and  the  arithmetical 
form  should  be  closely  connected  at  this  step  :  the  one  explains  the  other. 
No  explanation  should  be  learned  as  a  formula. 

5.  Divide  21  cakes  equally  among  3  children. 
How  many  will  each  receive  ?     (Picture  figures.) 

At  $7  each,  how  many  lamps  can  be  bought  for 
$21? 

I  have  $21  to  spend  for  3  birthday  presents. 
If  I  divide  the  money  equally,  what  must  I  pay 
for  each  ? 

One  of  the  three  equal  parts  of  21  cents  is  how 
many  cents  ? 

21  cents  contains  7  cents  how  many  times? 


16  ELEMENTARY  ARITHMETIC. 

Make  a  problem  for  each  of  these  forms  : 
£  of  21  =  7.      21  -r-  7,  3  times. 

6.  How  much   must   Harry  pay  for  3  rubber 

balls,  if  each  costs  7  cents  ? 

00.00000  OGOOOOO  ooooooo 

One  ball  costs  7  cents ;  3  balls  will  cost  3  times  as  much. 
Three  times  7  cents  are  21  cents. 
Slate  work :     7  cents,  cost  of  1  ball. 

3  (number  of  times  7-cents  are  used). 
21  cents,  cost  of  3  balls. 

At  $7  each,  what  will  3  rugs  cost  ?  (Make  a 
picture  for  this  problem.) 

How  many  7-dollars  must  you  pay  for  the  rugs? 

Each  make  a  problem  for  this  form  :  3x7=21. 

If  there  are  7  peas  in  a  pod,  how  many  peas  in 
3  such  pods  ?     (Picture.) 

7.  21  cubes  are  how  many  three-cubes  ? 

§§&&  000  000.  @00  000  000  ,00S 

7  three-cubes  are  how  many  ? 
21  is  how  many  3's  ?    21  =  7  threes.     21  --3  =  7. 
7  threes  are  how  many  ?    7  threes  =  21.    7x3  =  ? 
3  is  what  part  of  21  ?  •  }  of  21  =  ?     Seven 
sevenths  of  21  =  ? 

How  many  3's  can  you  take  out  of  21  ? 
Begin  with  21  and  subtract  3's. 
Begin  with  3  and  add  by  3's  to  21. 


NUMBERS  FROM  TWENTY  TO   THIRTY.         17 

Some  sparrows  were  in  the  maple  tree  ;  7,  which 
was  I  of  the  number,  flew  down.  How  many  were 
there  in  the  tree  at  first  ? 

8.  Make  a  picture  and  give  the  written  form 
for  each  of  the  following  problems  : 

A  gardener  takes  21  plants  to  market,  and  sells 
only  one  seventh  of  them  ;  how  many  does  he  sell  ? 

Give  21  shells  to  7  children ;  how  many  will 
each  receive  if  their  shares  are  equal  ? 

Anna  gathered  3  wild  roses  from  each  of  7 
branches  of  a  rosebush  ;  how  many  did  she  gather 
in  all  ? 

At  3  cents  each,  how  many  penholders  can  you 
get  for  21  cents  ? 

Divide  21  pansies  equally  among  mother,  sister? 
and  aunt ;  how  many  will  each  receive  ? 

Make  problems  for  the  following  forms  : 

7  cents  )  21  cents  7  )  21  cents 

~3~times  3  cents 

Answer  the  questions  you  have  asked,  giving 
slate  work  in  full. 

9.  Divide  22  balls  into  two  equal  groups. 

22  balls  are  how  many  eleven-balls  ? 
2  eleven-balls  are  how  many  balls  ? 
22  equals  how  many  elevens  ? 
22  =  two  ll's,  or  22-  11  =  2. 


18  ELEMENTARY  ARITHMETIC. 

11  balls  are  what  part  of  22  balls  ?  11  is  what 
part  of  22  ?    J  of  22  =  ? 

2  times  11  balls  are  how  many  ?     2xll  =  ? 
22  peaches  are  how  many  times  11  peaches  ? 

10.  22  balls  are  how  many  two-balls  ? 

00  00  00  QQ  QQ  QQ  00  AQ 
00  00  00 

11  two-balls  are  how  many  ? 

11  twos  are  how  many  ?     11x2  =  ? 

22  equals  how  many  2's  ?     22  =  eleven  2,s. 

22-2  =  11. 

2  balls  are  what  part  of  22  balls  ? 

2  is  what  part  of  22  ? 

Divide  22  bananas  equally  among  11  children  ; 
how  many  will  each  receive  ?  What  part  of  the 
whole  will  each  receive  ? 

11.  Make  problems  for  : 

3  oranges  )  21  oranges        3  )  21  oranges 

each  receives 

If  I  have  21  oranges  and  wish  to  give  3  oranges  to  each, 
etc. 


Copy 

and  learn 

22- 
22- 

21- 
21- 

-11=  2. 

-  2=11. 

-  7=  3 
-3=7. 

2  x  11  =  22. 
11  X    2  =  22. 

3  X    7  =  21 
7  x    3  =  21. 

22  -  11  =  11. 

i  of  22  =  11. 
21  -    7  =  14. 

J  of  21  =    7. 

NUMBERS  FROM   TWENTY   TO   THIRTY.         19 

12.  Divide  23  into  twos. 

oo  oo  oo  oo  oo  oo  oo  oo 
ooooooo 

23  equals  how  many  2's  ?  (Eleven  twos  and 
the  half  of  one  two,  or  111  twos.)  23  —  2  =  111. 
Ill  x  2  =  ? 

At  2  cents  a  yard,  how  many  yards  of  fancy 
paper  can  you  buy  for  23  cents,  if  you  spend  all 
the  money  ?  (As  many  yards  as  there  are  2's 
in  23.) 

13.  Divide  23  apples  equally  between  two  boys. 
What  part  of  the  whole  number  will  each  receive  ? 
How  many  will  each  receive  ? 

First  boy,       OOOOOOOOOOOd 
Second  boy,  OOOOOOOOOOOd. 

Each  receives  \  of  23  apples,  which  is  111  apples. 

Divide  23  sheets  of  paper  equally  between  2 
girls.  What  part  of  all  the  paper  will  each  receive  ? 
How  many  sheets  will  each  get  ? 

Ill  twos  less  111  ones  =  ?  23  contains  2  how 
many  times  ?     23  contains  111  how  many  times  ? 

14.  24  equals  how  many  twelves  ?     24  -r- 12  =  ? 

□□□□□□□□□□□□ 
Dnnnnnnannna 

2  twelves  are  how  many  ?    2  x  12  =  ? 
12  is  what  part  of  24  ?    \  of  24  =  ? 


20  ELEMENTARY  ARITHMETIC. 

A  dozen  is  what  part  of  24  ? 

Roy  bought  two  dozen  pieces  of  colored  crayon, 
and  used  \  of  them  the  first  term  of  school.  How 
many  did  he  use  ? 

15.  24  equals  how  many  twos  ?     24  ~  2  =  ? 

□□  "□□  □□  DD  □□  □□ 
DD  DD  DD  DD  DD  DD 

12  twos  are  how  many  ?     12  x  2  =  ? 

2  is  what  part  of  24  ?     One  twelfth  of  24  =  ? 
One    twelfth  of    24    cherries    are    how   many 

cherries  ? 

Show  with  objects  the  difference  between  one 
twelve  and  one   twelfth. 

24  cherries  are  how  many  times  2  cherries  ? 

At  2  cents  each,  what  will  a  dozen  eggs  cost  ? 

4 of  12  =  ?    &ofl  =  ? 

16.  24  is  how  many  8's  ?     24  -fr*  8  =  ? 

□□□nannn      □□□□□□□□ 
□□□□□□□□ 

3  eights  are  how  many  ?     3x8  =  ? 
8  is  what  part  of  24  ?     £  of  24  =  ? 
Count  24  by  8's.     Subtract  by  8's. 

24  nails  are  how  many  times  eight  nails  ? 
Give  24  nuts  to  3  boys.     How  many  will  each 
receive,  if  the  nuts  are  divided  equally?    (Picture.) 


NUMBERS  FROM  TWENTY  TO   THIRTY,         21 

17.  Divide  24  into  8  equal  groups. 

DDD  □□□  □□□  □□□ 
DDD  DDD  DDD  DDD 

24  equals  how  many  3's  ?     24  -f-  3  =  ? 
8  threes  equal  how  many  ?     8x3=? 

3  is  what  part  of  24  ?  1  of  24  =  ? 
Count  24  by  3's.  Subtract  by  3's. 
|  of  24  lemons  equals  how  many  ? 

Divide  a  quire  of  paper  (24  sheets)  equally  among 
8  pupils.     How  many  sheets  will  each  receive  ? 

Mary  learned  3  lines  of  a  poem  each  day  for  8 
days.     How  many  lines  of  poetry  did  she  learn  ? 

How  many  3-spools  can  you  take  out  of  a  box 
containing  24  spools  ? 

Some  children  were  gathering  golden-rod.  They 
found  that  they  had  gathered  in  all  24  branches. 
They  divided  equally,  and  each  had  3  branches. 
How  many  children  were  there  ? 

Make  problems  for  the  following  forms : 

24  -T-  8  =  3.        24  cents  -f-  3  =  8  cents.        3  x  8  =  24 

18.  24  equals  how  many  6's  ?     24  -f-  6  =  ? 

iiiiii  iiiiii  iiiiii  iiim 

4  sixes  are  how  many  ?     4x6  =  ? 
6  is  what  part  of  24  ?    \  of  24  =  ? 

Begin  with  6  and  add  6's  until  you  have  24. 


22  ELEMENTARY  ARITHMETIC. 

Henry  read  6  pages  of  his  new  book  on  Monday, 
6  on  Tuesday,  6  on  Wednesday,  and  6  on  Thursday. 
How  many  pages  did  he  read  ? 

George  walked  6  miles  each  day  for  four  days. 
How  many  miles  did  he  walk  ? 

Divide  24  maple  leaves  equally  among  4  girls. 
How  many  will  each  get  ?  (Picture  and  written 
form.) 

At  4  cents  each,  how  many  oranges  can  you  get 
for  24  cents  ?     (Picture  and  written  form.) 

19.    24  equals  how  many  4's  ?     24  -r-  4  =  ? 

mi  mi  mi  mi  mi  mi 

6  fours  are  how  many  ?     6x4  =  ? 

4  is  what  part  of  24  ?     \  of  24  =  ? 

Add  by  4's  to  24. 

At  4  cents  a  spool,  what  will  6  spools  of  thread 
cost? 

At  5  cents  a  spool,  how  many  spools  of  thread 
can  be  bought  for  24  cents  ? 

5  cents  )  24  cents. 

4  times  (4  cents  remaining). 
I  can  bny  4  spools  of  thread  and  have  4  cents  left. 

Make  a  problem  for  each  of  the  following  forms : 

24  nuts  -f-  6  nuts  =  4.  6  x  4  =  24. 

24  nuts  -^6  =  4  nuts. 


NUMBERS  FROM   TWENTY  TO    THIRTY.         23 

Represent  -  by  objects: 

One  six,  one  sixth  of  six,  one  sixth  of  1,  one  sixth  of  24. 

Add  J  of  21  to  J  of  24.         j'of  22  +  J  of  24  =  ? 

21  +  3x2  +  2-7  =  ?      i  of  24 +  6  =  how  many  3's ? 

20.  25  cents  are  how  many  5-cents  ?  25^5  =  ? 
5x5  =  ?    I  of  25  =  ? 

Peaches  are  selling  at  2  for  5  cents.  How  many 
can  you  buy  for  25  cents  ?  (Picture.)  If  you  can 
get  2  for  one  5-cents,  how  many  can  you  get  for 
five  5-cents  ? 

Divide  25  into  twos.  25  equals  how  many  twos  ? 
12  twos  and  half  of  one  two  are  how  many  ?  12| 
twos  are  how  many  ones  ?  25  contains  2  how 
many  times? 

John  bought  some  molding  for  picture  frames 
at  2  cents  a  foot.  He  spent  25  cents.  How  many 
feet  did  he  buy  ?     (Picture.) 

Make  problems  for : 

2  cents  )  25  cents  12J  times  2  =  25. 

\2\  times 

21.  Draw  upon  your  slate  25  circles  to  repre- 
sent cents.  Separate  this  25  into  12,s.  25  equals 
how  many  12's  ? 

Note.  All  common-sense  forms  of  expression  should  have  credit,  as : 
two  twelves  and  one  of  another  twelve ;  two  twelves  and  one  twelfth  of 
twelve ;  2^  twelves. 

Helen  has  25  cents  to  spend  for  lace  at  12  cents 
a  yard  ;  how  many  yards  can  she  buy  ? 


24  ELEMENTARY  ARITHMETIC. 

lyd.  OOOOOOOOOOOG 

lyd.  OOOOOOOOOOOO  O^jd. 

(She  can  buy  as  many  yards  as  there  are  12's 
in  25.) 

At  12  cents  a  foot,  how  many  feet  of  gilt  mold- 
ing can  be  bought  for  25  cents  ?     (Picture.) 

22.  What  will  2^  feet  of  silver  wire  cost  at  12 
cents  a  foot  ?     (Picture.) 

Make  problems  for : 

12  cents  )  25  cents  2^  times  12  =  25. 

2-j^  times 

Divide  25  feet  of  kite  string  equally  between 

two  boys ;  what  is  each  one's  share.     (Picture.) 

Make  a  problem  for  : 

2  )  25  pineapples 
each  receives 

I  paid  25  cents  for  2  pounds  of  butter ;  what  is 

that  a  pound  ? 

23.  Divide  25  into  threes. 

OOO      OOO      OOO  OOO 
OOO      OOO      OOO      OOO      o 

25  equals  how  many  threes  ?  (8|  threes,  or  8 
threes  and  \  of  one  three.) 

25  -s-  3  =  ?     8)  x  3  =  ? 
At  3  cents  a  pound,  how  many  pounds  of  salt 
can  you  buy  for  25  cents  ? 


NUMBERS  FROM   TWENTY  TO   THIRTY.        25 

24.  Divide  25  into  eights. 

oooooooo         25  e(iuals  how  many 

OOOOOOOO  eights?      (3    eights    and 

OOOOOOOO  O     one  of   another  eight.) 

25  +  8  =  ?    31  x  8  =  ?    8  )  25 

At  8  cents  a  pound,  how  many  pounds  of  rice 
can  you  buy  for  25  cents  ? 

25.  Divide  25  sticks  of  candy  equally  among 
8  boys.  How  many  will  each  receive  ?  (Make  a 
picture  to  show  this.)  Each  will  receive  what 
part  of  the  candy  ? 

Divide  25  crackers  equally  among  three  chil- 
dren.    (Picture.)     How  many  will  each  receive  ? 

Three  boxes  of  strawberries  cost  25  cents.  How 
much  is  that  a  box  ? 

8  spools  of  basting  thread  are  worth  25  cents. 
How  much  is  that  for  each  spool  ? 

26.  Divide  25  into  fours. 

OOOO  OOOO  OOOO 
OOOO  OOOO  OOOO  o 

25  equals  how  many  4's  ?  25  ~-  4  =  ? 
6|  x  4  =  ? 

Spend  25  cents  for  colored  paper  at  4  cents  a 
sheet.     How  many  sheets  can  you  buy  ? 


26  ELEMENTARY  ARITHMETIC. 

27.   Divide  25  into  sixes. 

OOOOOO   OOOOOO 
OOOOOO   OOOOOO  O 

25  equals  how  many  6's  ?  25  -*■  6  =  ? 
4|  x  6  =  ? 

At  6  cents  a  quart,  how  many  quarts  of  milk 
can  you  get  for  25  cents  ? 

Put  25  quarts  of  cherries  into  4  boxes.  How 
many  quarts  will  each  box  contain  if  you  divide 
them  equally  ?     (Picture.) 

George  gives  his  pony  25  ears  of  corn  in  6  days. 
How  much  is  that  a  day,  if  the  same  amount  is 
given  each  day  ?  (Picture.)  How  much  will  the 
horse  get  the  first  day?  This  is  what  part  of 
25  ears? 

28.     REVIEW 

3x8=?  4  x  6J  =  ?  1  of  26  =  ?  |  of  23  =  ? 

7x3=?  6x4j  =  ?  2x13  =  ?  J  of  25  =  ? 

4x6=?  24  -f-  3    =  ?  J  of  26  =  ?  J  of  26  =  ? 

3  X  8£  =  ?  25  -j-  3    =  ?  J  of  21  =  ?  \  of  25  =  ? 

Make  problems  for : 

i  of  25  =  12£.        25  -f-  2  =  12£.        3  X  8  =  24. 
24  ~-  3  =  8.        24  +  8  =  3. 

Give  the  written  form  in  answer  to  each  problem. 


NUMBERS  FROM  TWENTY  TO   THIRTY.         27 

29.  Take  27  cards  ;  separate  them  into  nines, 

DDDDDDDDD      DaQQQQQQQ 
DDDDDDDDD 

27  cards  equal  how  many  nine-cards  ? 
27  equals  how  many  9's  ?     27  -4-  9  =  ? 
3  nines  are  how  many  ?     3x9  =  ? 
9  is  what  part  of  27  ?     J  of  27  =  ? 
Count  27  by  9's.     Subtract  9's  from  27  to  0. 
At  $9  each,  what  will  3  clocks  cost  ?     (Draw 
picture.) 

30.  27  equals  how  many  3's  ?     27  +  3  =  ? 

ODD    DDD   DDD    DDD    DQQ 
DDD    DDD   DDD   DDD 

9  threes  are  how  many  ?     9x3  =  ? 
3  is  what  part  of  27  ?     One  ninth  of  27  =  ? 
Count  27  by  3's. 

One  ninth  of  27  cents  is  how  many  cents? 
At  $3  each,  what  will  9  ostrich  feathers  cost  ? 
(Picture.) 

Make  problems  for  these   forms   about   things 
that  grow  on  trees  : 

3  x  9  =  27.  9  X  3  =  27.  $  of  27  =  9. 

5x5  =  25.        25  4-5=    5.         27-9  =  3. 


28  ELEMENTARY  ARITHMETIC. 

31.  28  buttons  are  how  many  7*8  ?     28  -j-  7  =  ? 

00000*0    0000000    0000000 
0000000 

4  sevens  equal  what  ?     4x7  =  ? 

7  is  what  part  of  28  ?     \  of  28  =  ? 

How  many  times  can  I  take  7  buttons  out  of  28 
buttons  ? 

28  contains  7  how  many  times  ? 

Take  \  of  28  buttons  away,  how  many  fourths 
will  be  left  ?     How  many  buttons  will  be  left  ? 

Make  a  problem  for  each  of  these  forms : 

28  -^  7  =  4.      4  x  7  =  28.      J  of  28  =  7. 
28  buttons  equals  how  many  four-buttons  ? 

0000    0000    0000    0000 
0000    0000    0000 

32.  28  equals  how  many  4's  ?     28  -f-  4  =  ? 
7  fours  are  how  many  ?     7x4  =  ? 

4  is  what  part  of  28  ?     One  seventh  of  28  =  ? 

Count  by  4's  to  28. 

How  many  miles  do  I  walk  in  7  days  if  I  walk 
4  miles  each  day  ? 

I  will  give  you  28  cents  to  spend  for  oranges. 
If  they  cost  4  cents  apiece,  how  many  can  you  get  ? 
(Picture.) 

A  baker  sold  28  loaves  of  bread  to  7  customers. 
How  many  loaves  will  each  receive,  if  the  bread  is 


NUMBERS  FROM   TWENTY   TO    THIRTY,         29 

sold  in  equal  shares  ?    What  part  of  the  whole  did 
each  buy  ? 

Separate  28  into  2  equal  groups. 

0000000000  0000000000 

0000  000^ 

REVIEW. 
3X9=?         27+9  =  ?         J  of  27  =  ?         J  of  29  =  ? 
4x7=?         28~7  =  ?         J  of  28  =  ?         J  of  28  =  ? 
4x7^  =  ?         27-r-3  =  ?         J  of  27  =  ?         \  of  29  =  ? 

Make  problems  for  : 

3  )_27        4  )_29_       7x4  =  28        4x7  =  28 
9  7± 

Give  the  written  form  in  answer  to  your  prob- 
lems.    Each  term  must  be  properly  labeled. 

33.  30  equals  how  many  tens  ? 

Q@@Q@©Q©@©       ©©©©©@©©©© 
©@©@ ©©©©©© 
3  tens  equal  what  ?    30  -f-  10  =  ? 
10  is  what  part  of  30  ?     3x10  =  ? 
How  many  times  10  in  30  ?     J  of  30  =  ? 
Give   30  marbles  to  3  boys.     How  many  will 
each  receive,  if  they  are  divided  equally  ? 

34.  30  equals  how  many  threes  ? 

G$$     $$$  tfrft  $$$   frfrfr 

W$     $$$     $$$     $$$     $$$ 

10  threes  equal  what  ?     30  ■*■  3  =  ?     10  x  3  =  ? 


30  ELEMENTARY  ARITHMETIC. 

3  is  what  part  of  30  ?     One  tenth  of  30  =  ? 
Count  30  by  3's. 

How  many  times  can  3  be  taken  out  of  30  ? 
How  many  wheels  have  10  tricycles  ? 
%  If  you  pay  3  cents  apiece  for  peaches,  how  many 
can  you  get  for  30  cents  ? 

35.  30  equals  how  many  6's  ? 

$$$$$$    $$$$$$    $$$$$$ 
******    ot*$$$$ 

5  sixes  are  how  many  ?     30  —  6  =  ?     5x6  =  ? 

6  is  what  part  of  30  ?     One  fifth  of  30  =  ? 
Add  by  6's  to  30.     Begin  with  30  and  subtract 

6's. 

•How  many  times  will  30  melons  fill  a  basket 
which  holds  6  melons? 

30  equals  how  many  fives  ? 

36.  Give  30  acorns  to  6  boys.     How  many  will    * 
each  receive  if  they  are  divided  equally  ? 

$$$$$  $$$$$  ifr£6fr£ 
$$$$$  $$$$$  $$$$$ 

6  fives  equal  what  ?     30-5  =  ?     6x5  =  ? 
5  is  what  part  of  30  ?     One  sixth  of  30  =  ? 
How  many  times  can  I  ride  for  30  cents,  if  one 
street-car  fare  is  5  cents  ? 


NUMBERS  FROM   TWENTY   TO   THIRTY.        31 

37.    Divide  30  cents  into  fifteens. 

OOOOOOOOOO    OOOOOOO0OO 
GGOOO  OOOOO 

30  cents  are  how  many  15-cents? 
15  cents  are  what  part  of  30  cents  ? 


38. 


REVIEW. 


At  10  cents  each,  how  many  pineapples  can  you 
get  for  30  cents  ? 

Mary  wishes  to  plant  some  pinks  in  a  triangular 
garden  bed.  How  many  plants  will  she  use  if  she 
plants  10  on  each  of  the  3  sides  ?     (Picture.) 

How  many  5-cent  pieces  in  30  cents  ?    (Picture.) 

A  church  is  lighted  by  5  lamps  of  6  burners 
each.     How  many  burners  in  all? 

George  planted  some  hyacinth  bulbs  in  5  boxes, 
planting  6  bulbs  in  each  box.  '  How  many  did  he 
plant  in  all  ? 

A  boy  walks  10  squares  in  30  minutes.  At  that 
rate,  how  long  is  he  in  walking  one  square  ? 

I  bought  4  verbenas  for  30  cents.  What  did 
each  plant  cost,  if  they  are  of  equal  value  ? 

Make  problems  for  the  following  forms  : 
30  h-  5  =  6.        30  ~  6  =  5.        J  of  30  =  6.        6  x  5  =  30. 
3  )  30  4  )  30  4 )  29  4  x  7£  =  30. 

To  ~7i  ~7£ 


32 


ELEMENTARY  ARITHMETIC. 


39.  Copy  and  learn  : 

21 -r-7=3.  3x7  =  ? 

21-r-3=7.  7x3  =  ? 

22-t-11=  2.  2  xll  =  ? 

22 -h  2=11.  11  x   2  =  ? 

24h-12=   2.  2  xl2  =  ? 

24-4-  2=12.  12  x    2  =  ? 

24-7-8=  3.  3x8  =  ? 


24 


24 -r-  3=  8. 


6=4. 


24-f-   4=   6. 


8x3  =  ? 
4x  6  =  ? 
6x4  =  ? 


27-7-   9=  3. 

27  -r-  3=   9. 

28-t-  2=14. 
28-7-14=  2. 
28-r-  7=  4. 
28+  4=   7. 


25 -7-5=   5.       5x5  =  ' 


30 


30-7-  5=   6. 


3x    9  =  ? 
9x3  =  ? 


14  x 

2x 

4.X 
7X 

30-f-15=  2.  2  x 
30 -T-  2=15.  15  x 
30  -f- 10  =  3.  3  x 
30-7-3=10. 
6=5. 


10  X 
ox 
6X 


2  =  ? 

14  =  ? 
7  =  ? 

4  =  ? 

15  =  ? 

2  =  ? 
10  =  ? 

3  =  ? 
0  =  ? 

5  =  ? 


40.    COMPARISON  OF  HALVES,  FOURTHS,  AND  EIGHTHS. 


/<% 

"#X 

l'k\ 

/•/&\ 

1/8/ 

\*/6  ) 

y% 

%y 

A  whole  melon  can  be  divided  into  how  many- 
halves  ?     How  many  fourths  ? 

Fold  a  paper  square  into  two  equal  triangles. 
One  of  the  triangles  is  what  part  of  the  whole 
square  ? 


HALVES,   FOURTHS,    AND  EIGHTHS.  33 

Fold  the  same  square  so  as  to  make  four  equal 
triangles.  What  part  of  the  whole  square  is  one 
of  the  small  triangles  ? 

I  is  equal  to  how  many  fourths? 

\  and  1  make  how  many  fourths  ? 

\  +  i  equal  how  many  fourths  ? 

Fold  your  square  so  as  to  make  eight  equal  tri- 
angles. One  of  the  triangles  is  what  part  of  the 
whole  square  ?  Two  of  the  triangles  are  what  part 
of  the  whole  ? 

If  three  of  the  triangles  were  cut  out  of  the 
square,  what  part  of  the  whole  would  be  left  ? 

1  of  the  square  is  equal  to  how  many  eighths  ? 

\  is  equal  to  how  many  ? 

1  are  equal  to  how  many  eighths  ? 

f  of  a  whole  cheese  are  equal  to  how  many 
eighths  of  the  cheese  ? 

I  +  1  are  how  many  eighths  ?     \  +  1  =  ? 

1  +  1  are  how  many  eighths  ? 

41.  From  your  folded  squares  find  the  answers 
to  the  following  questions : 

i  +  f-  !-*.  i-h  i-h 

t  +  i.  t-i  I—'*-  i~l 

i  +  f.  !-±.  i-f.  i-l 

42.  Draw  upon  your  slate  a  square;  divide  it 
into  eight  equal  oblongs,  and  find  from  the  slate 
the  answers  to  the  following  questions  : 

SE 


34  ELEMENTARY  ARITHMETIC. 


2  times  \  =  ? 

3 

X|=?       4  X  i  =  ? 

5x|  =  how 

many  wholes  ? 

2  times  |  =  ? 

2 

x|=?      3x|=? 

3xf  =  how 

many  wholes  ? 

2  times  |  =  ? 

2 

Xf=?       2X|=f 

2x5  =  how 

many  wholes  ? 

4xi  =  ? 

3x  1  =  ?              i 

of  £  =  ? 

4XJ  =  ? 

£of£  =  ?              2 

X  f=? 

2xj  =  ? 

iofi  =  ?              4 

x  i  =  ? 

Mary  made  a  cake  for  tea ;  half  of  it  was  eaten, 
and  the  remainder  was  divided  equally  among  four 
visitors.  What  part  of  the  whole  cake  did  each 
wisitor  receive? 

George  had  a  ball  of  twine  for  his  kite  ;  he  used 
;hB!lf  of  it,  and  divided  the  remainder  equally  be- 
tween two  other  boys.  What  part  of  the  whole 
(ball  of  twine  did  each  boy  get  ? 

43.  Take  two  equal  squares  of  paper.  Fold 
'each  into  four  equal  smaller  squares ;  call  them 
square  crackers,  and  give  them  to  four  children, 
-so  that  they  shall  have  equal  shares.  What  part 
of  the  two  large  squares  does  each  child  receive  ? 
What  part  of  one  square  ? 

Note  to  the  Teacher.    Distribute  all  the  parts  of  one  square  first. 

To  how  many  children  did  you  give  the  two 
squares  ?  One  of  the  four  equal  parts  of  anything 
is  called  what  ? 


HALVES,  FOURTHS,   AND  EIGHTHS.  35 

Place  the  small  squares  together  again  so  as 
to  form  the  two  large  squares. 

i  of  2  squares  is  what  part  of  one  of  the  squares? 
I  of  2  pies  =  ?     I  of  2  apples  =  ?     \  of  2  melons  =  ? 

Divide  2  sticks  of  candy  equally  among  four 
boys.  What  part  of  the  whole  will  each  boy 
receive  ?     What  part  of  one  stick  is  that  ? 

44.  Take  three  equal  squares  of  paper.  Divide 
these  equally  among  four  children.  (Fold  each  into 
four  smaller  squares.)  What  part  of  the  three 
large  squares  does  each  child  receive  ?  What  part 
of  one  square  ? 

Into  how  many  equal  parts  did  you  divide  the 
three  squares  ?  One  of  these  equal  parts  is  called 
what  ? 

Place  the  small  squares  together  again  so  as  to 
form  the  three  large  squares  you  had  at  first.  \  of 
3  squares  is  what  part  of  one  square  ? 

Find  what  part  \  of  3  tooth-picks  is  of  one  whole 
tooth-pick. 

Divide  3  oranges  equally  among  4  boys.  What 
part  of  the  3  will  each  receive  ?  \  of  3  is  what 
part  of  1  ? 

Plant  3  potatoes  in  4  hills.  If  you  divide  them 
equally,  what  part  of  1  potato  will  be  in  each  hill  ? 
(Make  a  picture  to  show  this.) 

Give  3  bananas  to  4  girls,  dividing  them  equally. 
How  many  will  each  girl  receive  ? 


36 


ELEMENTARY  ARITHMETIC. 


Divide  23  melons  equally  among  4  boys.  What 
is  each  boy's  share  ?     (Picture.) 

I  wish  to  put  27  quarts  of  blackberries  into 
4  jars,  putting  the  same  number  of  quarts  into 
each.     How  many  quarts  will  each  jar  contain  ? 

45.     HALVES,   THIRDS,   AND   SIXTHS. 


M>   <fe 


One  third  of  an  orange  is  equal  to  how  many 
sixths  ? 

One  half  is  how  many  sixths  ? 

Fold  a  square  of  paper  into  two  equal  oblongs  ; 
one  of  the  oblongs  is  what  part  of  the  whole  ? 

Measure  and  draw  (parallel  to  the  line  made  by 
folding)  lines  which  shall  divide  the  paper  square 
into  three  equal  oblongs.  One  of  these  oblongs, 
made  by  drawing,  is  what  part  of  the  whole 
square  ? 

How  does  one  of  these  oblongs  compare  in  size 
with  |  the  square  ?     Which  is  larger,  \  or  \  ? 

A  third  and  half  of  a  third  will  make  what  part 
of  the  whole  square  ? 


HALVES,    THIRDS,   AND   SIXTHS.  37 

Fold  your  square  into  six  equal  oblongs.  One 
of  the  oblongs  is  what  part  of  the  whole  square  ? 

|  are  what  part  of  the  whole  ?  |  is  equal  to  how 
many  sixths  ? 

|  are  what  part  of  the  whole  ? 

Take  away  |  of  the  square ;  how  many  sixths 
are  left  ? 

46.  Draw  an  oblong  on  your  slate ;  divide  it 
into  six  equal  oblongs.  One  of  these  is  what  part 
of  the  whole  ?  Three  of  the  small  oblongs  are 
what  part  of  the  large  one  ? 

Look  at  your  drawing  and  find  the  answers  to 
these  questions  : 

|  and  I  are  how  many  sixths  ?  §  +  1  are  how 
many  sixths  ?     \  +  I  are  how  many  sixths  ? 

i  +  4  =  ?  *  +  *  =  ?  *-#  =  ?  f-4  =  ? 

§  +  i  =  ?  £  +  #  =  ?  *-*  =  ?  *-*  =  ? 

*  +  §  =  ?  t  +  f=?  t-i  =  ?  *-*  =  * 

4xi  =  ?  3xi  =  ?  6xi  =  ?  3x}  =  f 

|  are  how  many  thirds  ?  |  are  how  many 
halves  ?     §  are  how  many  thirds  ? 

47.  A  grocer  bought  a  cheese,  of  which  he  sold 
on  Monday  %  and  on  Tuesday  |.  What  part  of  the 
whole  cheese  remained  unsold  ? 

Henry  is  24  miles  from  home.  In  returning, 
he  rides  |  of  the  distance  on  his  bicycle,  §  on 
horseback,  and  walks  the  remainder  of  the  dis- 
tance.    How  many  miles  does  he  walk? 


#8  ELEMENTARY  ARITHMETIC. 

12  cents  is  half  my  money  ;  how  many  cents 
have  I?  Two  times  the  half  of  anything  equals 
what  ? 

6  cents  is  \  of  Ella's  money ;  how  many  cents 
has  she  ?     3  times  \  equals  what  ? 

Find  I  of  2.  Take  two  squares.  Fold  each  into 
three  equal  oblongs.  Divide  these  two  squares 
equally  among  three  children.  One  child  receives 
what  part  of  the  whole  ? 

Place  the  oblongs  so  as  to  form  the  two  squares 
again. 

|  of  2  squares  is  what  part  of  one  square  ? 

I  of  2  is  what  part  of  1  ? 

|  of  2  cakes  is  what  ?     I  of  2  pineapples. 

Divide  2  pies  equally  among  three  visitors ; 
how  much  will  each  receive  ?     (Picture.) 

48.  Put  2  pints  of  milk  into  3  cups,  so  that 
each  cup  shall  contain  the  same  quantity  as  the 
others.     How  much  in  each  ? 


Frank  picked  23  quarts  of  cherries  ;  he  kept  I  of 
them,  and  divided  the  remainder  equalty  between 
two  neighbors.    How  many  quarts  did  each  reecive  ? 


GILLS,  PINTS,   QUARTS,   AND  GALLONS.         3g\ 

A  quart  of  milk  is  how  many  pints  ? 

A  pint  is  what  part  of  a  quart  ? 

At  3  cents  a  pint,  what  will  a  quart  of  milk", 
cost? 

Four  gills  make  a  pint.  How  many  gill  bottles 
can  be  filled  from  a  pint  of  oil  ? 

1  gill  is  what  part  of  a  pint  ?  2  gills  are  what  • 
part  of  a  pint  ? 

A  soup  ladle  holds  2  gills.     How  many  times  - 
can  you  fill  it  from  a  pint  of  soup  ?     How  many 
times  from  a  quart? 

If  2  gills  of  lemon  extract  are  worth  25  cents, . 
what  is  1  gill  worth,  at  the  same  rate  ? 

George  sold  six  3-gill  glasses  of  lemonade.. 
How  many  pints  did  he  sell? 

It  takes  4  quarts  to  fill  a  gallon  measure ;  one- 
quart  is  what  part  of  a  gallon  ?  2  quarts  are 
what  part  of  a  gallon  ? 

At  8  cents  a  quart,  what  will  41  quarts  of 
vinegar  cost? 

How  many  1-gallon  jugs  will  be  needed  to  hold 
28  quarts  of  maple  molasses  ? 

How  many  quart  cans  will  be  needed  to  hold 
4  gallons  of  raspberries? 

4  gills  (gi.)  =  1  pint  (pt.). 
2  pints         is  1  quart  (qt.). 
4  quarts       =  1  gallon  (gal.). 


40  ELEMENTARY  ARITHMETIC. 

Liquids,  such  as  milk,  vinegar,  and  molasses, 
-are  measured  by  these  measures.  This  way  of 
rmeasuring  is  called  Liquid  Measure.  Name  other 
liquids  measured  in  this  way. 

49.    MISCELLANEOUS    PROBLEMS. 

1.  How  many  3-cents  in  27  cents  ? 

2.  Ella  found  4  eggs  each  day  for  a  wTeek ;  how 
many  dozen  did  she  find  ? 

3.  How  many  petals  have  6  violets,  if  each 
flower  has  5  petals  ? 

4.  John  worked  four  weeks,  and  earned  a  dollar 
each  working  day ;  his  brother  earned  half  as 
much  ;  what  did  each  earn  ? 

5.  Emma  had  3  dimes  ;  she  spent  6  cents  for  a 
pencil,  and  for  the  remainder  she  bought  3  plants 
for  the  schoolroom ;  what  did  each  plant  cost,  if 
they  were  of  equal  value  ? 

6.  27  feet  is  three  times  the  length  of  a  ladder; 
what  is  its  length  ? 

7.  Mary  made  25  sponge-cakes  ;  she  saved  5  to 
take  to  school,  and  divided  the  remainder  equally 
among  4  brothers  and  sisters ;  how  many  did  each 
receive  ? 

8.  Divide  2|  dozen  crackers  equally  among  5 
boys. 

9.  At  12J  cents  a  can,  what  will  2  cans  of  corn 
cost? 


FROM   THIRTY   TO   ONE  HUNDRED. 


41 


10.  I  bought  3  pounds  of  raisins  for  28  cents. 
How  much  is  that  a  pound  ? 

11.  Lemons  are  selling  at  20  cents  a  dozen. 
What  is  §  of  a  dozen  worth  ? . 

12.  Add  \  of  27  to  \  of  28.  3x7  +  6=  how 
many  9's.  One  fifth  of  25  +  6  =  \  of  what ! 
3  x  9  +  (?)  =  30.  6  x  5  -  10  is  the  half  of 
what  ?     3  times  one  fifth  of  30  +  3  =  ? 

50.  WRITING    NUMBERS. 
FROM   THIRTY   TO    ONE   HUNDRED. 


it  ' 


g  i 

fig 


Si 


§9IMilli9lllMffllliriil 

Thirty-one    Thirty-two     Thirty-three       Thirty-four  Thirty-five 


Three  Tens    Six  Ones         Three  Tens    Seven  Ones      Three  Tens    Eight  Ones 


Thirty-six  Thirty-seven 

Three  Tens         Nine  Ones 


I! 


Thirty-eight. 


Thirty-nine 

Find  the  counters  and  write  the  figures  for  three 
tens  and  one  one  ;   three  tens  and  two  ones. 

Add  one  each  time,  and  represent  by  figures 
through  three  tens  and  nine. 


42  ELEMENTARY  ARITHMETIC. 

Three  tens  and  two  ones  are  how  many  ones  ? 
Three  tens  and  five  ones  are  how  many  ones  ? 
Three  tens  and  nine  ones  are  how  many  ones  ? 
Read  these  numbers :  31,  32,  33,  34,  35,  36,  37, 
38,  39. 

51.  Add  1    to   three  tens  and  9  ones.     How 
40  many    tens   are    there  ?      Write    the 

pourTenB         number  in  figures. 

Four  tens  are  how  many  ones  ? 
Count    by    ones,    beginning    with 
Forty  forty,  until  you  have  four  tens  and 

nine  ones. 

Read  these  numbers  :  40,  41,  42,  43,  44,  45,  46, 
47,  48,  49. 

Tell  the  number  of  tens  and  ones  each  repre- 
sents. 

52.  Copy  and  read  the  following  : 


10 

30 

48 

42 

31 

17 

22 

44 

29 

24 

13 

27 

11 

23 

16 

16 

18 

36 

33 

32 

40 

41 

21 

26 

19 

15 

37 

14 

12 

45 

The  right-hand  figure  of  each  of  these  numbers 
expresses  what  ? 

When  a  number  is  expressed  by  two  figures,  the 
right-hand  figure  always  stands  for  ones,  and  the 
left-hand  figure  for  tens. 


FROM  THIRTY   TO    ONE   HUNDRED. 
Write  in  words  : 


30 

19 

23 

42 

18 

35 

28 

47 

33 

39 

44 

17 

11 

14 

48 

47 

22 

36 

43 


50 


53.  With  your  counters  in  hand,  add  1  to  4 
tens  and  9  ones. 

How  many  tens  and  ones  have  you  ?  Write  the 
figures  for  this  number.  5  tens  are  how  many 
ones  ? 

Count  by  ones,  beginning  with 
fifty,  until  you  have  five  tens  and 
nine  ones.  Write  each  number  as 
you  count.  Eead :  50,  51,  52,  53, 
54,  55,  56,  57,  58,  59. 

Write  the  tens  and  ones  each  represents. 

56  is  how  many  tens  and  ones  ?  56  is  how 
many  ones  ? 

Show  with  your  counters  the  number  of  tens 
and  ones  in  58.     Show  the  number  of  ones. 


Fifty 


60 

Six  Tens 


54.    Find  six  tens  with  your  sticks.     Express 
six  tens  in  figures. 

Begin  with  sixty,  and  count 
by  ones  through  sixty-nine.  Ex- 
press each  number  in  figures  as 
you  count. 


44 


ELEMENTARY  ARITHMETIC. 


Read  these  numbers  as  tens  and  ones  :  60,  61, 
62,  63,  64,  65,  66,  67,  68,  69. 

How  many  ones  in  six  tens  and  four  ones  ?  In 
six  tens  and  nine  ones  ? 

Six  tens  are  how  many  more  than  five  tens  ? 

55.    Find  seven  tens,  and  express  this  number 
in  figures. 

Count  by  ones,  beginning  with 
seventy,  until  you  have  seven 
tens  and  nine  ones. 

Express  each  number  in  figures 
as  you  count.  Read  :  70,  71,  72,  73,  74,  75,  76, 
77,  78,  79 

Copy  and  read  the  following : 


70 

Seven  Tens 


Seventy 


55 

73 

36 

69 

79 

43 

64 

37 

63 

60 

53 

34 

46 

48 

77 

51 

35 

71 

75 

70 

28 

15 

27 

17 

57 

19 

59 

78 

72 

62 

Write  the  last  column  in  words. 

Write  in  figures  a  number  which  is  ten  more 
than  30 ;  one  that  is  ten  more  than  50 ;  ten  more 
than  60 ;  ten  less  than  70. 

Sixty  is  how  many  more  than  50  ?  20  is  how 
many  more  than  10  ?  20  is  how  many  less 
than  30? 


FROM   THIRTY   TO   ONE   HUNDRED.  45 

How  many 


80 

Eight  Tens 


Eighty 


56.    Add  one  to  7  tens  and  9  ones 
tens   have   you  ?      Write   the 
number  in  figures. 

Count  by  ones  through  eight 
tens,  and  nine  ones.  Write 
each  number  in  figures.  80, 
81,  82,  83,  84,  85,  86,  87,  88,  89. 

How  many  tens  and  ones  does  the  third  number 
from  the  left  represent  ? 

Lay  down  the  counters  for  each  of  these  num- 
bers :  84,  88,  81,  87,  and  89. 

How  many  ones  in  eighty-nine  ?  How  many 
tens  and  ones  in  89  ones  ? 

5  7.  Add  1  to  eight  tens  and  9  ones.  How  many 
tens  are  there  ?     Write  the  number  in  figures. 

Count  by  ones,  and  write 
the  numbers  through  nine 
tens  and  nine  ones.  90,  91, 
92,  93,  94,  95,  96,  97,  98, 
99. 

Tell  how  many  tens  and  "ones  each  represents. 

Ninety  ones  are  how  many  tens  and  ones. 

97  ones  are  how  many  tens  and  ones  ? 

How  many  ones  in  9  tens  and  3  ones  ?  9  tens 
and  5  ones  ?  9  tens  and  8  ones  ?  8  tens  and  6 
ones  ?     7  tens  and  4  ones  ?     5  tens  and  9  ones  ? 

99  is  the  largest  number  which  can  be  expressed 
by  two  figures. 


90 

Nine  Tens 


Hlffllfll 


Ninety 


ren  T( 

II 


46  ELEMENTARY  ARITHMETIC. 

58.   With  your  counters  in   hand,  add  one  to 
100  9  tens  and  9  ones.     How 

Ten  Ten*.  many     tens     have     you  ? 

How    many    ones,    beside 
the  ten    tens  ?      Ten   tens 

One  Hundred.  ^       ^^       QnQ      lmn(Jre(l# 

One  hundred  is  how  many  tens  ?  How  many 
ones  ?  (Untie  the  bundles.)  One  ten  is  what 
part  of  ten  tens  ? 

Find  one  one  (beside  the  one  hundred)  with  the 
sticks.  Place  it  on  your  slate  or  against  the 
blackboard. 

Find  one  ten  with  the  sticks  also,  and  place  it  to 
the  left  of  the  one  one. 

Place  the  one  hundred  to  the  left  of  the  one  ten. 

Write  under  the  one  one  the  figure  which  stands 
for  1  one. 

Write  under  the  one  ten  the  figure  which  stands 
for  1  ten. 

Write  the  figure  1  under  the  one  hundred  of 
sticks. 

Point  to  the  figure  1  which  means  1  one ;  to  the 
figure  1  which  means  1  ten;  to  the  figure  1  which 
means  1  hundred. 

Eemove  the  1  one.  In  its  place  write  the  figure 
which  means  no  ones.  Remove  the  1  ten ;  in  its 
place  write  the  figure  which  stands  for  no  tens. 
How  many  ones,  tens,  and  hundreds  have  you  ? 


ADDITION  AND   SUBTRACTION,  47 

Bead  the  number,  beginning  at  the  left. 
1  hundred  is  written  to  the  left  of  the  tens. 
100  equals  ten  tens,     100  is  one  hundred  ones. 

59.   ADDITION    AND  SUBTRACTION. 

REVIEW  OF  NUMBERS  FROM  TEN  TO  TWENTY. 

Find  all  the  sums  which  can  be  formed  by  add- 
ing any  two  numbers  below  ten. 

Read  sums  only. 
84967598598787897639 


2  8 

5 

9 

4 

6 

3 

7 

9 

7 

5 

3 

7 

6 

6 

9 

5 

4 

9 

6 

7  7 

9 

7 

8 

9 

5 

9 

8 

6 

7 

6 

8 

5 

3 

9 

6 

4 

4 

8 

8  9 

4 

3 

9 

2 

4 

4 

7 

3 

2 

7 

4 

3 

8 

8 

5 

9 

7 

6 

Subtract'the  lower  number ;  give  results  only : 
9     10     13     15     14     12     16     15     17     13    14     18 


4 

6 

9 

8 

6 

,7 

9 

9 

8 

6 

9 

9 

12 

11 

17 

13 

16 

15 

14 

17 

12 

15 

16 

11 

8 

7 

9 

8 

7 

7 

5 

13 

5 

6 

12 

6 

60.   Separate  21  cubes  into  two  unequal  groups. 

liiiii,lP®[S'iP(SPiSlBii?fi!iSiS    0009999 

If  you  take  the  smaller  number  out  of  the  whole, 
what  will  remain  ? 

If  you  take  the  larger  number  from  the  sum  of 
the  two  parts,  what  will  remain  ?  21  —  7  =  ? 
21  -  14  =  ? 


48  ELEMENTARY  ARITHMETIC. 

21  cubes  are  how  many  more  than  7  cubes  ? 

010000100 

Ella  has  21  blocks  and  Frank  has  7 ;  how  many 
more  has  Ella  than  Frank  ? 

If  you  take  out  of  Ellas  blocks  a  number  equal 
to  Frank's,  what  will  be  left  ? 

What  is  the  difference  between  21  and  7  ? 

21  is  14  more  than  what  number  ? 

If  my  desk  is  7  inches  longer  than  my  slate,  the 
slate  is  how  many  inches  shorter  than  the  desk  ? 
(Measure.) 

61.    20  books  4-  3  books  equals  how  many  books? 

20  nails  +  5  nails  =  ?  20  ones  +  3  ones  =  ? 
2  tens  +  7  tens  =  ? 

Write  these  numbers  and  add  them.  Add  ones 
first  in  each  example. 


20 

24 

30  20  30  40  20 

32 

43 

6 

2 

9  10  40  50  16 

7 

4 

Finding  the  sum  of  ttco  or  more  numbers  is  called 
Addition* 

The  sign  of  Addition  (+)  is  called  plus.  The 
numbers  between  which  it  is  placed  are  to  be 
added. 

The  sign  (=)  means  equals.  8  +  6  =  14,  is 
read,  8  plus  6  equals  14. 


ONE  HUNDRED    TO   FIVE  HUNDRED.  49 

Add  12,  49,  and  33. 

^2  Add  ones  first,  naming  results  only ;  thus,  3,  12, 

49        14  ones  (1  ten  and  4  ones).     Write  the  4  ones  in 
33        ones'  place  below  the  line,  and  add  the  1  ten  with 
—       the  tens.    4,  8,  9  tens.    Write  9  tens  in  tens'  place. 
The  sum  is  94. 

Copy  and  add : 

(1)     (2)     (3)     (4)     (5)     (6)     (7)     (8)       . 
12      25      36      44      16      29      34     28 
14      10      11      14      25      16      23      16 
16      12141012113951 

(9)  (10)  (11)  (12)  (13)  (14)  (15)  (16) 
28  39  28  18  29  67  58  45 
16  14  26  54  14  17  13  16 
J*_3131723_2_414 

62.    WRITING    NUMBERS. 
ONE   HUNDRED   TO   FIVE   HUNDRED. 

Take  the  counters  and  find  1  hundred,  2  tens, 
4  ones. 

What  number  have  you  ?  How  many  ones  in 
all  ?     Write  the  number. 

Find  with  the  sticks  and  write  : 

1  hundred,  3  tens,  7  ones.  1  hundred,  9  tens,  0  ones. 

1         «        5     "     6     "  1         "        6     "     5     " 

1         "        8     <k     3     "  1         "        1     "      1  one. 

1        «        l     «     2     "  1        "        0     "     0  ones. 

How  many  ones  in  the  first  number  ? 

4E 


50  ELEMENTARY  ARITHMETIC. 

Tell  how  many  ones  in  each  of  the  other 
numbers. 

Which  is  greater,  6  ones  or  5  tens  ?  One  hun- 
dred or  6  tens  ? 

How  many  tens  make  one  hundred  ? 

Begin  with  1  hundred,  and  write  in  figures  all 
the  numbers  through  1  hundred,  9  tens,  and  9 
ones. 

Add  1  to  199  ;  how  many  tens  have  you  ?  How 
many  ones  ?     Write  the  number. 

134  ®^#   What  does  the  figure  4  mean  in 

216      the  number  134?     Because  the  figure  4 

159      means  4  ones,  it  is  written  in  ones'  place. 

178  For  what  do  the  6,  9,  and  8  stand  ?  Ones 
are  always  written  in  ones'  place. 

What  does  the  figure  3  mean  in  the  first  num- 
ber ?     Why  is  it  written  in  tens  place  ? 

The  figure  1  in  the  second  number  means  what  ? 

The  5  and  7  stand  for  what  ? 

Tens  are  always  ivritten  in  tens'  place. 

The  figure  1  in  the  first  number  means  what  ? 

The  figure  2  in  the  second  number  means 
what? 

Because  the  figure  1  means  one  hundred,  it  is 
written  in  hundreds'  place. 

In  what  place  is  the  figure  2  written  ? 

Hundreds  are  always  ivritten  in  hundreds'  place 


ONE  HUNDRED    TO   FIVE  HUNDRED. 


51 


64.    Ones'  place,    tens'  place,    and    hundreds' 
place  make  ones'  period. 

*  DlIM1     Porir>H 

Copy  and  read  these  numbers  : 

124  101  116  173  119  112 

186  111  105  113  191  121 

210  198  115  131  109  200 

181  106  137  103  129  201 

2  in  tens'  place  means  how  many  ? 
place  means  how  many  ? 

Find  with  the  counters  and  write  the  numbers 
from  200  to  300. 


ill  ij  si 

W  T3    ft       El    A  O    Pi 

13  4 
2  16 
15       9 

2  in  ones' 


65.   Write  in  figures  : 


3  hundred,  0  tens,  0  ones. 
2         "        2     "     2     " 
5        "        0     "     0     " 


2  hundred,  5  tens,  3  ones. 
1         "        6     "     7     " 

3  "        7     "     9     " 

4  «        3     «     8     " 

The  first  number  equals  how  many  ones  ? 
Which  is  greater,  3  hundred  or  3  tens  ? 

5  hundred  is  how  many  more  than  3  hundred  ? 
Read  the  following : 

311  222  202  314  384  404 

210  333  212  341  448  401 

413  331  221  413  444  309 

125  313  211  431  414  319 

414  is  how  many  more  than  313?  330  is  how 
many  more  than  230  ?  450  is  how  many  less 
than  500? 


52  \     ELEMENTARY    ARITHMETIC. 

66.     Copy  and  add  : 


(1) 

(2) 

(3) 

(*) 

(5). 

,  (6) 

CO 

(8) 

(9) 

79 

99 

89 

38 

38 

97 

38 

56 

2 

13 

03 

13 

04 

16 

49 

17 

57 

12 

66 

25 

25 

72 

72 

21 

82 

23 

49 

21 

51 

41 

62 

52 

11 

41 

41 

63 

11 

11 

12 

13 

12 

11 

12 

11 

93 

10) 

(11) 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

76 

39 

55 

59 

50 

98 

78 

72 

34 

64 

34 

24 

34 

59 

57 

15 

45 

75 

23 

73 

75 

72 

34 

12 

61 

41 

22 

12 

33 

21 

14 

31 

12 

25 

16 

12 

12 

11 

11 

11 

11 

10 

11 

15 

57 

67.    ADDING   AND    SUBTRACTING   BY    ENDINGS. 
Write  ten  numbers    ending  in  0 ;    add  one   to 
each  of  these  numbers. 

10  20     30      40      50      60      70      80      90     100 

a     li     ii     1*  i     i     l      i 

With  what  figure  does  each  sum  end? 
Write  ten  numbers    ending    in  1 ;    subtract    1 
from  each  number. 

11  21      31      41      51      61      71      81      91      101 

_1     _1     J    J.     _1     J       1       1       1         1 

With  what  figure  does  each  answer  end  ? 
Add  1  to  all  numbers  below  100,  which  end  in 
1 ;  in  2,  3,  4,  5,  or  6. 

If  you  subtract  1  from  numbers   ending  in  2, 
with  what  figure  does  each  answer  end  ? 


ADDITION   AND  SUBTRACTION.  53 

Write  10  numbers  ending  in  3,  and  subtract  1 
from  each  number. 

One  from  numbers  ending  in  9  gives  what  end- 
ing figure  ? 

Write  a  table  subtracting  1  from  numbers  end- 
ing in  0. 

68.    8  +  1  and  1  +  8. 

Add,  giving  first  the  ending  figure  of  the  sum, 
and  then  the  whole  sum. 

8      18     28      38      48      58      68      78      88     98 
111111111       1 


1 

11 

21 

31 

41 

51 

61 

71 

81 

91 

8 

8 

8 

8 

8 

8 

8 

8 

8 

8 

Add,  beginning  at  the  left. 

1,  8,  1,   1,  8,   1,   1,  8,   1,   1,  8,  1,  8,  1,  1,  8. 

8,  1,   1,   8,   1,   1,   1,   8,   1,   1,  8,   1,  8,  1,   1,  1. 

9,  6,  3,  1,   1,   1,   8,   1>   8,   1,   1,   8,   1,  1,   1,  8. 
6,  8,   4,   1,   1,  8,   1,   1,   1,  8,   1,   8,   1,  1,   1,  8. 

69.  9  +  1  and  1  +  9. 

Add  9  to  numbers  ending  in  1. 

1      11      21      31      41      51      61      71  81  91 
9999999999 


64  ELEMENTARY  ARITHMETIC. 

Add: 

1,   9,  9,  1,  1,  9.  1,  9,  1,  9,  1,  9,  1,  9,  1,   9. 

9,   1,  1,  9,  9,  1,  1,  9,  9,  1,  1,  9,  1,  9,  9,   1. 

8,  8,  4,  1,  9,  1,  9,  8,  1,  1,  9,  1,  9,  1,  9. 

9,  8,  3,  9,  1,  1,  9,  1,  9,  9,  1,  1,  9,  5,  1. 

8,    7,   5,   9,   1,   8,   1,    1,   9,   1,   1,   9,   1,   9,   9,   1. 

Add,  beginning  at  the  bottom  of  the  line. 

(1)    (2)    (3)    (4)    (5)    (6)    (7)    (8)    (9)  (10)  (11)  (12) 


9 

1 

1 

9 

2 

9 

8 

9 

8 

9 

9 

1 

1 

9 

1 

1 

8 

1 

1 

1 

1 

1 

1 

9 

9 

1 

8 

9 

1 

9 

8 

3 

9 

1 

9 

1 

1 

9 

1 

9 

8 

1 

1 

6 

1 

9 

1 

1 

1 

1 

8 

1 

1 

1 

9 

9 

1 

9 

1 

5 

8 

1 

1 

9 

1 

1 

1 

1 

9 

1 

8 

4 

1 

9 

9 

1 

9 

8 

1 

1 

9 

1 

1 

1 

9 

9 

1 

1 

1 

1 

8 

9 

1 

9 

9 

9 

1 

1 

1 

9 

1 

9 

1 

.1 

1 

1 

1 

1 

1 

4 

1 

5 

8 

7 

7 

3 

1 

5 

9 

7 

9 

8 

9 

9 

1 

4 

5 

7 

3 

7 

6 

6 

9 

8 

9 

6 

9 

9 

8 

9 

5 

7 

5 

6 

4  O.     Slate  Exercises. 
(1)     (2)     (3)     (4)     (5)     (6)     (7)      (8)      (9)    (10) 


99 

99 

99 

88 

98 

19 

99 

89 

99 

91 

91 

11 

11 

11 

91 

91 

99 

19 

11 

19 

11 

11 

11 

98 

19 

11 

11 

91 

99 

91 

19 

88 

19 

11 

91 

18 

11 

11 ' 

11 

19 

99 

91 

81 

99 

11 

89 

19 

99 

11 

11 

11 

19 

90 

11 

19 

10 

89 

11 

91 

91 

11 

11 

18 

11 

89 

91 

11 

11 

98 

19 

81 

19 

11 

31 

11 

19 

15 

81 

14 

16 

93 

46 

99 

39 

99 

94 

47 

98 

68 

46 

75 

95 

61 

99 

71 

67 

98 

79 

98 

98 

ADDITION  AND  SUBTRACTION.  55. 

71.     MISCELLANEOUS    PROBLEMS. 

1.  George  had  24  nails;  he  gave  4  to  Henry  and* 
4  to  James.  How  many  did  he  give  away,  and  how 
many  had  he  left  ? 

(mi)(im)mmnmnm 

Slate  work : 

24  nails,  George  has.  4  nails,  gave  to  Henry.. 

8  nails,  George  gave  away.  4  nails,  gave  to  James. 

16  nails,  George  had  left.  8  nails,  gave  to  both. 

2.  A  watch  cost  $24,  and  a  chain  cost  $8.    How 
much  more  did  the  watch  cost  than  the  chain? 

00000000OOOOOOOOOOOOOOOO^ 
OOOQOOOO 

$24,  cost  of  watch. 
8,  cost  of  chain. 
$16,  difference  between  cost  of  watch  and  chain. 

The  watch  cost  $16  more  than  the  chain. 


3.  A  kite  cost  24  cents,  and  this  is  8  cents  more 
than  the  cost  of  a  top.  What  was  the  cost  of  the 
top? 

4.  A  picture  costs  24  cents;  Mary  wishes  to  buy 
it,  but  has  only  8  cents.  How  many  more  cents 
must  she  have  to  buy  the  picture  ? 

Is  there  any  difference  between  the  number  of 
cents  .Mary  has,  and  the  number  of  cents  the  pic- 
ture costs  ?     How  do  you  find  the  difference  ? 


56  ELEMENTARY  ARITHMETIC. 

Slate  work : 

24  cents,  cost  of  picture. 

8  cents,  Mary  has. 
16  cents,  difference  between  24  cents  and  8  cents. 
The  number  of  cents  Mary  needs  to  add  to  8  cents  to  be 
able  to  buy  the  picture. 

5.  Margaret  gathered  21  pond  lilies  :  she  gave 
7  to  Mamma,  and  took  7  to  school  to  her  teacher. 
How  many  had  she  left  ? 

6.  Grace  wrote  11  lines  in  her  copy-book  on 
Monday,  7  on  Tuesday,  and  7  on  Wednesday ; 
how  many  lines  did  she  write  in  all  ? 

7.  Grapes  are  selling  at  3  pounds  for  25  cents; 
what  is  that  a  pound  ? 

8.  One  week  a  chairmaker  made  31  parlor  chairs 
and  8  office  chairs.  He  sold  7  out  of  the  whole 
number.     How  many  had  he  left  to  sell  ? 

9.  A  boy,  having  50  cents,  paid  9  cents  for  a 
ball ;  he  afterwards  found  8  cents  ;  how  many 
cents  had  he  then  ? 

10.  Two  rooms  each  rent  for  $12  a  month,  and 
two  shops  each  rent  for  $9  a  month ;  what  is  the 
rent  of  all  for  a  month  ? 

11.  A  hotel  keeper  bought  24  boxes  of  straw- 
berries of  one  person  and  6  of  another ;  one  third 
of  the  whole  was  used  for  breakfast ;  how  many 
boxes  were  left  ? 

12.  Alfred  bought  a  music  box  for  30  cents  ; 


ADDITION  AND   SUBTRACTION.  57 

after  mending  it,  he  sold  it  for  9  cents  more  than 
it  cost  him.     How  much  did  he  receive  for  it  ? 

Slate  work : 

30  cents,  cost  of  music  box. 
9  cents,  gained  by  selling, 
cents,  money  received  for  the  box. 

(Whenever  there  is  any  difficulty  in  understanding  a 
problem,  it  should  be  pictured.) 

The  cost  was  how  much  less  than  the  selling  price? 

The  difference  between  the  cost  and  the  selling 
price  was  how  many  cents  ? 

If  the  cost  is  9  cents  less  than  the  selling  price, 
how  would  you  make  it  equal  to  the  selling  price  ? 

Make  problems  for  the  following  forms  : 

31  +  9  =  40.  41  -2.  51  +  8.  69  -  2. 

72.    ADDITION   AND    SUBTRACTION   OF   2. 

Make  a  table  adding  2  to  numbers  ending  in  2. 
Add  3  and  4  to  numbers  ending  in  2. 
Subtract  2  from  numbers  ending  in  2. 

2      12      22      32      42      52      62      72      82      92 
22222        2        2      j2      J?      J? 

Take  2  from  numbers  ending  in  3  ;  what  is  the 
ending  figure  ?     2  from  numbers  ending  in  9  ? 


11 

21 

31 

41 

51 

61 

71 

81 

91 

101 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

58  ELEMENTARY  ARITHMETIC. 

What  is  the  ending  figure  when  you  take  2  from 
numbers  ending  in  1  ? 

Subtraction  of  1  and  2  from  numbers  ending  in 
any  one  of  the  digits. 

(1)  10  11  22  33  44  55  66     77  88  99 

(2)  11  12  23  34  45  56  67  78  89  91 

222222_2_2J2J2 

Add  5  and  6  to  numbers  ending  in  2. 

Read  the  ending  figure  first,  then  the  whole  sum. 

2     12     22    32    42     52     62      72     82      92     102 

5  _5     _5     j>     _5       5       5       5       5       5        5 

2     12    22     32    42      52     62      72     82      92     102 

6  6      6      6       6       6       6       6       6        6        6 

73*    Slate  Exercises,  2  +  5,  2-f  6,  and  Review. 

(1)      (2)      (3)     (4)     (5)     (6)     (7)     (8)     (9)    (10) 
15      16      16      81      16      22      15      51      69      66 


62 

11 

52 

11 

12 

11 

61 

21 

11 

22 

21 

69 

21 

16 

51 

91 

21 

16 

19 

11 

19 

21 

11 

62 

21 

16 

16 

12 

11 

91 

11 

11 

18 

21 

16 

12 

12 

61 

51 

16 

81 

16 

61 

11 

92 

61 

81 

21 

26 

12 

11 

62 

21 

14 

11 

21 

11 

11 

12 

61 

15 

25 

16 

27 

11 

11 

12 

14 

19 

29 

65 

97 

89 

57 

69 

99 

68 

67 

65 

97 

97 

78 

83 

80 

99 

78 

98 

96 

86 

83 

74.  7  +  2  and  2  +  7. 

2     12    22     32    42     52      62      72     82     92     102 

7777777777         7 


ADDITION  AND  SUBTRACTION.  59 

Add: 

2,   7,   1,   9,   1,   2,   7,   1,   1,   9,   2,   7,   1,  2,  7. 

9,   8,   2,   1,   9,   1,   2,   7,   1,   2,   7,   1,   9,  1,   2,   7. 

6,   6,   5,   2,   1,   2,   6,   1,   1,   2,   5,  2,   1,  2,   7. 

Slate  Exercises,  2  +  7  and  7  +  2,  and  Review. 

(1)      (2)     (3)     (4)    (5)     (6)     (7)     (8)     (9)    (10) 


97 

87 

72 

11 

67 

79 

11 

71 

11 

19 

12 

12 

21 

77 

21 

21 

71 

27 

79 

71 

71 

11 

17 

22 

17 

11 

26 

12 

21 

27 

27 

61 

92 

11 

72 

26. 

12 

71 

97 

92 

12 

26 

11 

79 

21 

52 

71 

27 

12 

19 

91 

12 

79 

21 

19 

21 

27 

12 

19 

11 

12 

71 

21 

11 

91 

12 

12 

91 

91 

91 

3 

22 

11 

92 

17 

74 

29 

18 

14 

11 

77 

98 

79 

98 

77 

28 

45 

77 

78 

79 

97 

89 

89 

78 

85 

75 

96 

84 

78 

89 

75.      MISCELLANEOUS    PROBLEMS. 

1.  Emma  spent  5  cents  for  a  watch-key,  and 
had  42  cents  left ;  how  much  money  had  she  at 
first? 

2.  Alice  paid  28  cents  for  a  reader,  \  as  much 
for  pencils,  and  \  as  much  for  paper ;  how  many 
cents  did  she  spend  ? 

3.  A  young  man  earned  $9  a  week,  and  spent 
$5  a  week  for  board  ;  how  much  did  he  save  in 
7  weeks? 

4.  On  a  journey  of  3  days  my  expenses  were 
$5,  $7,  and  $6.  When  I  started  I  had  a  20-dollar 
bill.     How  much  money  had  I  when  I  returned  ? 


60  ELEMENTARY  ARITHMETIC. 

5.  A  fruit  dealer  sells  \  of  a  dozen  oranges,  and 
has  24  left ;   how  many  had  he  at  first  ? 

6.  Mary  made  a  wall-pocket,  and  sold  it  for  30 
cents  ;  this  is  more  than  it  cost  her  ;  it  is  9  cents 
more.     What  did  it  cost  her  ? 

Slate  work : 
30  cents,  selling  price. 
9  cents,  difference  between  cost  and  selling  price, 
cents,  cost. 

30  cents  is  how 'much  more  than  the  cost? 
The  cost  is  how  much  less  than  30  cents  ? 

7.  A  boy  shot  an  arrow  39  feet  up  the  road, 
and  another  21  feet  down  the  road  ;  how  far  must 
he  walk  to  get  them  ?     (Two  answers.) 

8.  If  a  gallon  of  oil  costs  30  cents,  what  is  the 
cost  of  half  a  gallon  ?     The  cost  of  a  quart  ? 

9.  George  made  a  sled  and  sold  it  for  68  cents ; 
this  was  8  cents  more  than  it  cost  him;  how  much 
did  it  cost  ? 

76.    WRITING    NUMBERS. 
HOW   TO    EXPRESS    NUMBERS    TO    ONE    THOUSAND. 

Find  with  the  counters  5  hundreds,  9  tens,  and  9 
ones.  Add  one  one.  How  many  hundreds  have 
you? 

Write  in  figures  6  hundreds.  Write  6  hundreds, 
4  tens  ;  6  hundreds,  5  tens,  and  2  ones. 

Find  7  hundreds.     Write  the  number  in  figures. 


EXPRESS  NUMBERS   TO   ONE   THOUSAND.       61 

Read  : 

643        611        721        505        707        606 


751 

610 

712 

689 

770 

660 

589 

601 

702 

799 

777 

66Q 

Which  is  the  greater  number,  659  or  569  ?  697 
or  769  ?     571  or  751  ? 

Find  8  hundreds.     Write  the  number  in  figures. 

Find  8  hundreds,  8  tens,  and  8  ones. 

Find  9  hundreds,  and  represent  the  number  by 
figures. 

Find  9' hundreds,  9  tens,  and  9  ones. 

Read  : 

845  984  901  991  999  880 
862  936  909  919  808  881 
933        847        990        900        888        818 

The  greatest  number  that  can  be  expressed  by 
three  figures  is  999. 

Add  1  to  999  ;  how  many  hundreds  have  you  ? 
Ten  hundreds  make  1  thousand. 

The  number  one  thousand  is  expressed  by  writ- 
ing the  figure  1  in  thousands'  place,  to  the  left  of 
the  hundreds. 

Ten  hundreds  equal  one  thousand. 

77.   8  +  2  and  2  +  8. 

Make  a  table,  adding  2  to  numbers  ending  in  8. 
Add  8  to  numbers  ending  in  2. 


62  ELEMENTARY  ARITHMETIC. 

Slate  Exercises,  8  +  2  and  2  +  8,  and  Review. 

(1)     (2)     (3)     (4)     (5)     (6)     (7)     (8)      (9)     (10) 


91 

98 

97 

89 

86 

82 

89 

78 

97 

95 

17 

12 

12 

28 

12 

29 

18 

22 

12 

12 

22 

81 

78 

82 

11 

81 

72 

89 

89 

79 

68 

27 

22 

29 

87 

28 

29 

21 

21 

21 

22 

92 

89 

91 

22 

12 

91 

98 

98 

80 

18 

18 

21 

18 

18 

19 

18 

10 

12 

28 

12 

82 

91 

82 

72 

81 

82 

82 

82 

92 

24 

22 

12 

26 

28 

28 

26 

29 

25 

16 

88 

69 

88 

95 

84 

45 

87 

87 

89 

86 

78 

99 

89 

69 

88 

97 

77 

74 

84 

88 

Add: 

(11)  27,  62,  29,  81,  28,  12,  75,  27,  88,  and  80. 

(12)  68,  22,  89,  21,  98,  12,  80,  28,  63,  and  99. 

78.   9  +  2  and  2  +  9. 


2 

12 

22 

32 

42 

52 

62 

72 

82 

92 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

19 

29 

39 

49 

59 

69 

79 

89 

99 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

Add: 

9,    2,  8,  2,  1,  9,  1,  9,  1,  9,  1,  9,  1,  9.  8,  2. 

6,    6,  9,  1,  9,  1,  9,  1,  6,  2,  2,  6,  1,  1,  7,  2. 

9,    9,  2,  2,  9,  1,  9,  1,  9,  9,  2,  9,  9,  2,  2,  2. 

8,   4,  9,  9,  2,  9,  1,  7,  2,  9,  2,  6,  2,  9,  2.  7- 


MISCELLANEOUS  PROBLEMS.  63 

Slate  Exercises,  2  +  9  and  9  +  2,  and  Review. 

(1)     (2)     (3)      (4)     (5)     (6)     (7)     (8)      (9)     (10) 


89 

89 

99 

89 

99 

29 

89 

82 

72 

89 

22 

28 

81 

29 

81 

69 

92 

97 

21 

21 

98 

12 

28 

92 

28 

22 

99 

21 

97 

99 

92 

79 

92 

99 

92 

89 

19 

99 

92 

'  92 

29 

29 

99 

29 

99 

29 

92 

92 

29 

29 

99 

92 

29 

92 

29 

92 

28 

29 

89 

92 

92 

99 

12 

91 

82 

99 

92 

91 

22 

91 

29 

29 

22 

22 

24, 

29 

19 

25 

94 

24 

54 

68 

49 

98 

67 

65 

65 

97 

18 

97 

97 

84 

79 

59 

89 

77 

86 

58 

48 

57 

Add: 

(11)  29,  79,  22,  98,  92,  29,  99,  92,  28,  99,  and  43. 

(12)  98,  82,  29,  99,  92,  29,  92,  96,  29,  64,  and  80. 

79.      MISCELLANEOUS    PROBLEMS. 

1.  John  sold  a  knife  to  Edgar  for  20  cents; 
this  is  less  than  John  paid  for  it ;  it  is  5  cents  less. 
What  did  John  pay  for  the  knife  ? 

Slate  work  : 

20  cents,  Edgar  paid  for  the  knife. 
5  cents,  difference  between  what  John  paid  and  what 
Edgar  paid, 
cents,  John  paid  for  the  knife. 

Edgar  paid  5  cents  less  than  John.  How  much 
more  did  John  pay  than  Edgar  ? 

2.  After  buying  3  pounds  of  sugar  at  9  cents  a 
pound,  I  had  25  cents  left ;  how  much  money  had 
I  at  first  ? 


64  ELEMENTARY  ARITHMETIC. 

3.  In  the  morning  session  of  school  there  are  3 
hours,  and  in  the  afternoon  session  2  hours  ;  how 
many  hours  in  a  school  week  ? 

4.  In  a  certain  school  there  are  9  girls  and  3 
times  #s  many  boys ;  how  many  boys  in  the  school, 
and  how  many  boys  and  girls  together  ? 

5.  In  building  his  chicken  house,  John  uses  72 
shingles,  and  needs  7  more  ;  how  many  should  he 
have  had  at  first  ? 

6.  A  peck  of  apples  costs  30  cents  ;  I  must  bor- 
row 9  cents  in  order  to  pay  for  them ;  how  much 
money  have  I  ?  (Picture  ;  compare  9  cents  with 
30  cents.) 

7.  Henry  bought  a  pair  of  skates  for  75  cents, 
and  sold  them  for  8  cents  less  than  he  gave  for 
them.     For  how  much  did  he  sell  them  ? 

8.  How  many  feet  of  rope  can  I  buy  for  30 
cents,  if  I  pay  3  cents  a  foot  ?  How  many,  if  I 
pay  5  cents  a  foot? 

9.  If  2  pounds  of  figs  cost  30  cents,  what  will  a 
pound  cost  ?     What  will  §  of  a  pound  cost  ? 

10.  In  30  lead  pencils,  how  many  packages  of 
half  a  dozen? 


CHAPTER  III. 

NUMBERS    FROM    THIRTY   TO    FORTY. 
1.    32  cents  are  how  many  eight-cents  ? 
OOOOOOOO       32  +  8  =  ? 
OOOOOOOO        4x8=? 
OOOOOOOO        0.  '  ,Mn 

OOOOOOOO         1S     at  Part  °*  ^  - 

I  wish  to  put  32  qt.  of  milk  into  cans  holding 
8    qt.   each;    how   many   cans    will   be    needed? 

Divide  32  qt.  of  milk  equally  among  4  cus- 
tomers.     How  many  quarts   will    each   receive? 

Make  problems  for  : 


)  32  cents. 

4,  8-cents  in  32  cents. 


)  32  cents  in  all. 

4  cents,  each  receives. 

32  cents  are  how  many  four-cents?     (Drawing.) 

32-4  =  ?     8x4  =  ?     |  of  32  =  ? 

Make  problems  for  : 

32  +  4  =  8.  8  x    4  =  32.  4  x  8  =  32. 

i  of  32  =  8.  iof32=    4. 

Give  the  written  work  in  answer  to  your  problems. 


66  ELEMENTARY  ARITHMETIC, 

2.  33  cents  are  how  many  times  11  cents  ? 
33  +  11  =  ?     3  x  11  =  ?     |  of  S3  =  t 

OOOO  OQOO  oooo  oooo 
oooo  oooo  oooo  oooo  o 

33  -4-  4  =  ?     8\  fours  are  how  many  ?     8\  x  4  =  ? 

Frank  is  33  miles  from  home.  If  he  should 
walk  at  the  rate  of  4  miles  an  hour,  how  long 
would  he  be  in  walking  the  whole  distance  ? 

3.  33  equals  how  many  8's  ? 

OOOOOOOO 

OOOOOOOO  33-8  =  ?    41  x  8  =  ?    4| 

OOOOOOOO         eights  are  how  many? 
OOOOOOOO   O 

At  8  cents  a  pound,  how  many  pounds  of 
crackers  can  you  buy  for  33  cents  ? 

Make  problems  for : 
33  ~  8  =  4J.      4J  times  8  =  33.     £  of  33  =  ?     i  of  33  =  ? 

Pack  33  qt.  of  ice-cream  in  4  cans  of  equal  size. 
How  many  quarts  will  each  can  contain  ? 

4.    REVIEW. 


4x    8    =? 

4£  X    8    =  ? 

32- 

-    4  =  ? 

T^  Of  33  =   : 

3  x  10£  =  ? 

3    x  11    =  ? 

33- 

-11  =  ? 

i  of  32  =  ? 

4  x    7|  =  ? 

6    x    5J  =  ? 

31- 

-    3=  ? 

£  of  33  =  ? 

2  x  16    =  ? 

8£  x    4    =  ? 

33- 

-    4=  ? 

£  of  31  =  ? 

A  freight  train  is  moving  at  the  rate  of  10  miles 
an  hour.  At  that  rate,  how  long  will  it  be  in  going 
31  miles  ? 


NUMBERS  FROM    THIRTY  TO  FORTY.  67 

What  will  8\  yd.  of  silk  cost,  at  $4  a  yard? 
33  pounds  of  honey  were  packed  in  8  jars  of 
equal  size  ;  how  many  pounds  in  each  jar  ? 
Make  problems  for  these  forms  : 

31  -^  3  =  10J.        31  -5-  2  =  15J.        i  of  31  =  10J. 
£  of  31  =  15£.        33  4-  4  =    8J.         J  of  33  =    8J. 

Give  the  written  work  for  your  problems. 

5.  35  is  how  many  sevens  ?  Draw  35  circles 
upon  your  slate  to  represent  cents  ;  divide  them 
into  7's. 

35-7  =  ?  5x7  =  ?  I  of  35  =  ?  7  is  what 
part  of  35  ? 

Draw  35  cents,  and  divide  them  into  5's. 

35  +  5  =  ?     7x5  =  ?    |  of  35  =  ? 

Make  a  problem  for :   |  of  35  =  5.     35  -f-  7  =  5. 

$5  is  £  of  my  money  :  how  much  money  have  I  ? 
Seven  times  \  are  how  many  sevenths  ? 

\  of  35  +  \  of  35  =  ?     35  -  \  of  35  =  ?    35  -  \  of  35  =  ? 

6.     REVIEW. 

34  -i-  2  =  ?       34  -f-    4    =  ?       8  x    4J  =  ?  J  of  34=? 

34  -f-  3  =  ?         7x5=?       2x17=?  J  of  35  =  ? 

35  _^  7  =  ?         3  *  Hi  .ss  ?       \  of  35  =  ?  4  x  8J  =  ? 

Ella  counted  7  red  leaves  on  each  of  5 
branches  of  a  maple  tree  ;  how  many  leaves  did 
she  count  ? 


68  ELEMENTARY  ARITHMETIC. 

A  shoe  merchant  sold  8  pairs  of  shoes  for  $34 ; 
how  much  was  that  a  pair  ? 

John  planted  35  currant  bushes,  planting  7  in  a 
row  ;  how  many  rows  were  there  ? 

Robert  raised  35  pumpkins,  and  sold  f  of  them; 
how  many  had  he  left  ? 

7.  Draw  36  triangles  and  divide  them  into 
twelves. 

36  equals  how  many  12's  ?  36  ~  12  =  ? 
3  x   12  =  ? 

12  is  what  part  of  36  ?     |  of  36  =  ? 

Give  36  roses  to  mother,  May,  and  Grace. 
How  many  will  each  receive  if  you  divide  them 
equally  ? 

Draw  36  triangles,  and  divide  them  into 
threes. 

36  equals  how  many  3's  ?    36-3  =  ?    12x3  =  ? 

3  is  what  part  of  36  ?     f2  of  36  =  ? 

How  many  3-cents  in  36  cents  ? 

Draw  36  melon  seeds  ;  divide  them  into  nines. 

36  equals  how  many  9's  ?     36  4-  9  =  ?     4x9  =  ? 

9  is  what  part  of  36  ?     36  -  \  of  36  =  ? 

18  is  how  many  fourths  of  36  ?  $9  is  \  of  my 
money  ;  how  much  money  have  I  ?  4  nines  are 
how  many  ones  ? 

Draw  36  seeds,  and  divide  them  into  fours. 

36  ~  4  =  ?     9x4  =  ?    I  of  36  =  ? 


NUMBERS  FROM   THIRTY  TO  FORTY.  69 

If  I  use  4  pounds  of  butter  a  week,  how  many 
pounds  shall  I  use  in  9  weeks  ? 
Make  problems  for  : 

36  +  4  =  9.  i  of  36  =  4  36  -^  9  =  4. 

Divide  36  nails  into  6  equal  groups.  36  -r-  6  =  ? 
6x6-? 

6  is  what  part  of  36  ?  At  6  cents  each,  how 
many  papers  of  needles  can  you  buy  for  36  cents  ? 

8.  Divide  37  shells  into  twelves  : 

37  is  how  many  12's  ?     37-*- 12  =  ?    3&  x  12  =#? 

At  12  cents  a  quart,  how  many  quarts  of  cran- 
berries can  you  get  for  37  cents  ? 

Divide  37  peaches  equally  among  3  boys.  How 
many  will  each  receive  ?     (Drawing.) 

Make  problems  for : 
3A-  X  12  =  37.      37  ^  12  =  3f*.      i  of  37  =  12J. 

9.  Divide  37  shells  into  threes  : 

($9®    ©<§0    00®    ©0®    000    000 
<8>0®    ©<SM$    00®    000    000   ®00    0 

37  is  how  many  3's  ?  37  +  3  =  ?  12i  x  3  =  ? 
A  of  37  =  ? 

At  $3  a  box,  how  many  boxes  of  oranges  can  be 
bought  for  $37  ? 


70  ELEMENTARY  ARITHMETIC. 

^  of  37  loaves  of  bread  is  how  many  loaves  ? 

Find  J  of  37  inches  of  lead  pipe,  \  of  37  gallons 
of  oil,  I  of  37  pounds  of  corn  meal. 

At  6  cents  a  pound,  how  many  pounds  of  hominy 
can  you  buy  for  37  cents  ?  At  $5  each,  how  many 
writing  desks  can  be  bought  for  $37  ? 

10.    review. 

12  x  3  =  ?       3^  X  12     =  ?       36  -T-  3  =  ?  J  of  36  =  ? 

9x4=?       6      x    6J   =?       36-t-9=?  J  of  37=? 

6  x  C  =  ?     12      x    3tV  =  ?       37  -T-  4  =  ?  J  of  36  =  ? 

4x9=?       4      x9J=?       37-t-3=?  £  of  37  =  ? 

1.  Alice  has  36  cents  to  spend  for  flowers.  If 
she  spends  12  cents  for  each  plant,  how  many  can 
she  buy  ? 

2.  Give  36  pinks  to  6  children.  How  many 
will  each  receive,  if  you  divide  them  equally? 

3.  At  12  cents  a  yard,  how  many  yards  of  oil- 
cloth can  you  buy  for  37  cents  ? 

4.  Horace  says :  "  Four  times  my  age  is  my 
father's  age."  How  old  is  his  father,  if  Horace 
is  9  years  old? 

5.  If  I  put  12  candles  on  each  of  3  birthday 
cakes,  how  many  candles  shall  I  use  ? 

6.  Find  \  of  37  ears  of  corn ;  i  of  37  heads  of 
cabbage. 

7.  Make  problems  for  these  forms,  about  things 
found  in  the  forest  : 

36  -f-  4  =  9.       9  x  4  =  36.        36  +  12  =  3.       36  ~  9  =  4. 


JS  UMBERS  FROM   THIRTY   TO  FORTY.  71 

8.    Make  problems  for  the  following  forms  and 
give  the  written  work  in  answer : 
6  x  6  =  36.      6  X  6£  =  37.      J  of  37  =  9J.      37  ^  4  =  9J 

11.  40  is  how  many  tens  ?  40  -  10  =  ? 
4  x  10  =  ?      \  of  40  =  ? 

40  is  how  many  fours  ?  40  h-  4  =  ?  10x4  =  ? 
h  of  40  =  ? 

Make  problems  for : 

40  -r-  4  =  10.         40  -h  10  =  4.         10  x  4  =  40. 

40  is  how  many  eights  ? 

Make  a  drawing  to  show  this.  Draw  leaves  of 
some  plant. 

40-8  =  ?     5x8  =  ?     8  is  what  part  of  40  ? 

At  Christmas,  40  pounds  of  candy  were  divided 
among  5  schools ;  how  many  pounds  did  each 
school  receive  ? 

40  is  how  many  fives  ?      40  —  5  =  ?     8x5  =  ? 

At  5  cents  a  loaf,  how  many  loaves  of  bread  can 
you  get  for  40  cents  ? 

12.  review. 
\  of  38  =  ?         i  of  40  =  ? 
J  of  39  =  ?         I  of  38  =  ? 
J  of  38  =  ?         i  of  40  =  ? 
i  of  39  =  ?         8x    5  =  ? 

1.  Mary  had  40  cents.  She  spent  J  of  it  for 
paper,  \  for  a  thimble,  and  1  for  a  bunch  of  violets- 
How  much  money  had  she  left  ? 


4  x  9|  =  ? 

40  ~  8  =  ? 

6  x  6J  =  ? 

38  -4-  4  =  ? 

6  x  6J  =  ? 

39  -r-  6  =  ? 

4  x  9i  =  ? 

38  h-  3  =  ? 

72  ELEMENTARY  ARITHMETIC. 

2.  If  39  gallons  of  coal-oil  are  used  in  4  months, 
how  many  gallons  at  that  rate  will  be  used  in  1 
month  ? 

3.  38  pounds  of  rice  lasted  a  camping  party  9 
weeks  ;  how  many  pounds  was  that  a  week  ? 

4.  How  many  hours  will  it  take  Albert  to  hoe 
40  rows  of  corn,  if  he  hoes  5  rows  in  an  hour  ? 

5.  Divide  40  sheets  of  drawing  paper  equally 
between  two  classes  of  a  school. 

6.  Make  problems  for  these  forms : 

£of40  =   8.      40-8   =   5.     J  of  38=   9J.     \  of  39=   9J 
38  -7- 3  =  12§.      6x6J  =  38.     2x19  =  38.       3x13  =  39. 

13.    Copy  and  learn  : 

1x2=2  1x3=3  1x4=4 

2x2=4  2x3=6  2x4=8 

3x2=6  3x3=9.  3x4  =  12 

4x2=8  4x3  =  12  4x4  =  16 

5x2  =  10  5x3  =  15  5x4  =  20 

6x2  =  12  6x3  =  18  6x4  =  24 

7x2  =  14  7x3  =  21  7x4  =  28 

8x2  =  16  8x3  =  24  8x4  =  32 

9x2  =  18  9x3  =  27  9x4  =  36 

10  x  2  =  20  10  x  3  =  30  10  x  4  =  40 

11  x  2  =  22  11  x  3  =  33 

12  x  2  =  24  12  x  3  =  36 


LONG    MEASURE.  73 

14.    REVIEW. 
MEASURING  LENGTH,  OR  LONG  MEASURE. 


What  is  the  length  of  the  first  line  ?  Of  the 
second  ?  The  length  of  the  first  line  is  what  part 
of  the  length  of  the  second  ? 

The  second  line  is  what  part  of  the  third  ? 

Cut  a  piece  of  paper  12  inches  long  and  1  inch 
wide.     Draw  a  line  12  inches  long. 

12  inches  make  a  measure  that  is  called  one  (?). 

How  many  six-inch  sticks  of  candy  can  you  cut 
from  a  stick  12  inches  long  ?  How  many  3-inch 
sticks  ?     3  inches  are  what  part  of  a  foot  ? 

How  many  4-inch  lead  pencils  can  be  made  from 
a  piece  of  lead  12  inches  long  ?  4  inches  are  what 
part  of  a  foot  ?     5  inches  ?     One  inch  ? 

How  many  feet  in  fifteen  inches  ?     In  eighteen  ? 

Draw  a  line  3  feet  long  ?  Three  feet  make  one 
yard.  Mention  some  things  that  are  sold  by  the 
yard.  How  many  inches  in  one  yard  ?  1  foot  is 
what  part  of  a  yard  ? 

15.  1  a  yard  is  how  many  inches  ?  How  many 
feet? 


74  ELEMENTARY  ARITHMETIC. 

J  of  a  yard  is  how  many  inches  ?     \  of  a  yard  ? 

12  inches  are  what  part  of  a  yard  ?     4|  inches  ? 

Ella  has  a  yard  of  silk  with  which  to  dress  4 
dolls  for  the  fair.  What  part  of  the  silk  shall  she 
use  for  each  dress,  if  she  divides  it  equally  ?  How 
many  inches  for  each  ? 

If  a  yard  of  ribbon  is  divided  for  badges  equally 
among  8  boys,  what  will  be  the  length  of  each 
piece  ? 

In  2  yards  how  many  feet  ?  In  3  yards  ?  How 
many  half  yards  in  2  yards  ?  How  many  in  3 
yards  ? 

16.  How  many  feet  tall  are  you  ?  What  is 
the  height  of  the  teacher's  table  from  the  floor  ? 
(Estimate  first,  and  then  measure.)  What  is  the 
length  of  the  table  ?  How  far  from  the  top  of 
your  desk  to  the  floor  ?  Height  of  the  transom 
from  the  floor?  Width  of  window  sash?  Height 
of  clock  from  the  floor  ?  Length,  in  feet,  of  front 
blackboard  ?  Length  of  room  ?  Width  of  room  ? 
Tie  a  knot  for  every  foot  in  a  piece  of  twine  6  feet 
long.     Tie  a  double  knot  for  every  yard. 

Estimate  length,  width,  and  height  of  things 
outside  of  schoolroom,  and  then  measure  :  height 
of  a  barrel ;  of  a  common  wooden  bucket ;  length 
of  an  ear  of  corn. 

12  inches  (in.)  =  1  foot  (ft.). 
3  feet  =  1  yard  (yd.> 


LONG    MEASURE.  75 

In  measuring  goods  sold  by  the  yard,  the 
yard  is  divided  into  halves,  fourths,  eighths,  and 
sixteenths. 

2\  inches  =  1  sixteenth  (^  yd.). 

2    sixteenths  (4£  in.)  =  1  eighth  (J  yd.). 
2    eighths  (9  in.)         =  1  quarter  (£  yd.). 
4    quarters  =  1  yard  (1  yd.). 

17.   Comparison  of  the  fractions  one  half,  one 

third,  one  fourth,  and  one  sixth. 

Into  how  many  equal  parts  is 
this  circle  divided  ? 

One  of  the  twelve  equal  parts 
of  anything  is  called  what  ?  One 
half  of  the  circle  is  how  many  of 
these  parts  ?  One  third  of  the 
circle  is  how  many  twelfths  of 
the  whole  circle  ?  |  is  how  many  twelfths  ?  |  is 
how  many  twelfths  ? 

Which  is  more,  §  of  a  cake  or  \  ?     \  or  \  ? 

Look  at  the  circle  and  find  the  answers  to  these 
questions  (or  cut  a  circle  from  paper,  fold  it  into 
halves,  then  into  sixths,  then  into  twelfths). 

I  and  I  are  how  many  twelfths  ?  |  and  I  are 
how  many  twelfths  V 

1+  i  =  ?  t  +  *  *■  T  #  +  A  =  ?  « ■  -  A  =  t 
£+£=?  *  +  4  =  ?  t  +  A  =  ?  *  -  A  =  * 
i  +  A  =*  ?       i  +  i  =  ?        *  -  A  =  ?        1-!=? 


76  ELEMENTARY  ARITHMETIC. 

18.  Alice  cut  out  1  of  a  cake  to  take  to  a 
picnic ;  her  mother  used  \  of  the  cake  for  tea. 
What  part  of  the  whole  cake  was  left  ? 

Edgar  used  \  of  a  ball  of  twine,  and  his  brother 
Carl  used  \  of  the  ball ;  what  part  of  the  whole 
ball  was  left  ? 

Look  at  the  circle,  or  draw  a  circle,  and  find 
answers : 

^  =  how  many  sixths  ?       Find  J  of  J  of  the  circle. 
^5  ss  how  many  fourths  ?     J  of  J  is  what  part  of  the  whole  ? 
*fc  =  how  many  halves  ?      J  of  J  is  what  part  of  the  whole  ? 

^  =  how  many  fourths  ?     J  of  } $  =  ?      J  of  ^  =  ? 
\%  s  how  many  sixths  ?       £  of  £  ==  ?        £  of  £  =  ? 

19.  i  is  found  in  ^  how  many  times  ?  i£  con- 
tains ^  how  many  times  ?  §  contains  ^  how  many 
times  ? 

2  times  \  are  how  many  wholes  ?  4  times  1  are 
how  many  wholes  ? 

3  x  ^  are  how  many  twelfths  ?  How  many 
wholes  ? 

4  x  f  are  how  many  wholes  ?     4  x  f  =  ? 
Which  of  these  forms  is  most  used  :   g  or  |  ? 

&  or  !? 


DRY  MEASURE.  77 

20.    DRY  MEASURE. 


Pint-  Quart.  Peck.  ^^^^ 

A'  quart  of  berries  is  how  many  pints  ? 

A  peck  of  beans  is  how  many  quarts  ? 

Eight  quarts  make  a  peck. 

Where  have  you  seen  these  measures  used? 
Name  some  things  which  you  have  seen  measured 
by  them. 

Half  a  peck  of  nuts  is  how  many  quarts  ? 

J  of  a  peck  is  how  many  quarts  ? 

4  quarts  of  berries  are  what  part  of  a  peck  ? 

6  quarts  are  what  part  of  a  peck  ? 

i  of  a  peck  of  oats  are  how  many  quarts  ? 

John  sowed  |  of  a  peck  of  blue-grass  seed ;  how 
many  quarts  were  left  out  of  a  peck  ? 

Four  pecks  make  a  bushel. 

21.   1  a  bushel  of  potatoes  is  how  many  pecks  ? 
1  of  a  bushel  are  how  many  pecks  ? 
Half  a  bushel  of  cranberries  is  how  many  quarts  ? 
Two  bushels  are  how  many  pecks  ? 
Estimate  the  capacity  of  a  box  or  basket  brought 
into  the  schoolroom. 

•11  bushels  of  walnuts  are  how  many  pecks  ? 


78  ELEMENTARY  ARITHMETIC. 

Henry  gathered  a  bushel  of  beans  from  his 
garden,  and  sold  half  of  them  for  25  cents  a  peck. 
How  much  money  did  he  receive  ? 

Grains,  fruits,  vegetables,  and  some  other  things 

that  are  not  liquids,  are  sold  by  these  measures. 

This  is  called  Dry  Measure. 

2  pints  (pt.)  =1  quart  (qt.). 
8  quarts  =  1  peck  (pk.). 

4  pecks  sb  1  bushel  (bu.). 

22.    MISCELLANEOUS   PROBLEMS. 

1.  How  many  feet  in  a  yard?  How  many 
inches  in  a  yard  ?  §  of  a  yard  is  how  many 
inches  ?     How  many  feet  ? 

2.  Early  in  the  spring  I  found  a  little  flower 
called  the  wake-robin ;  each  one  had  3  petals ; 
eleven  such  flowers  have  how  many  petals  ? 

3.  We  have  a  measure  which  holds  just  8 
quarts ;  what  is  the  measure  called  ?  Shell  a 
peck  of  corn  ;  how  many  quarts  have  you  ? 

4.  A  party  of  boys  went  nutting  and  gathered 
2\  pecks  of  nuts ;  how  many  quarts  is  that  ? 

5.  32  quarts  of  strawberries  are  how  many 
gallons  ? 

6.  At  9  cents  a  yard,  how  many  yards  of  mus- 
lin can  you  buy  for  38  cents  ? 

7.  How  many  spools  of  thread  can  I  buy  for 
35  cents,  at  5  cents  a  spool  ?  How  many  at  4 
cents  a  spool  ?     How  many  cents  remaining  ? 


ADDITION  AND   SUBTRACTION  OF  8.  79 

8.  §  of  24  acres  of  land  is  planted  in  sugar- 
corn,  fe  in  potatoes,  \  in  oats,  and  the  remainder 
in  meadow  ;  how  many  acres  in  meadow  ? 

9.  A  man  is  rowing  down  the  river  8  miles  an 
hour ;  at  that  rate  how  long  will  he  be  in  going 
34  miles? 

10.  At  4  cents  a  pound,  how  many  pounds  of 
oatmeal  can  you  get  for  39  cents  ? 

11.  Give  3  pecks  of  corn  to  four  horses,  divid- 
ing it  equally ;  what  part  of  the  3  pecks  will  each 
receive  ? 

12.  How  many  quarts  in  5  pecks? 

A  common  wooden  bucket  holds  how  many 
pecks  ? 

Such  questions  have  very  little  meaning  unless  the  measures  have  been 
used  by  pupils  until  they  have  some  idea  of  their  comparative  size  and 
value. 

23.    ADDITION    AND    SUBTRACTION    OP   3. 

Make  a  table,  adding  3  to  numbers  ending  in  3. 
What  is  the  ending  figure  of  each  sum  ? 

Add  3  to  numbers  ending  in  4. 

Subtract  3  from  numbers  ending  in  3;  from 
numbers  ending  in  4. 

Add  3  to  numbers  ending  in  5.  What  is  the 
ending  figure? 

53  +  3=?         64  +  3  =  ?         73  —  3=?         84  —  3  =  ? 


80  ELEMENTARY  ARITHMETIC. 

A  ,,  5  +  3   AND    3  +  5. 

Ada : 

5,    3,    2,    5,    3,    2,    5,    3,    2,   3,    5,    2,  5,    3,  2. 

9,    6,    3,    2,    3,    5,    1,    2,    2,    5,    2,    5,  3,    2,  5. 

8,    7,    3,    2,    5,    3,    1,    2,    4,    3,    2,    3,  5,    1,  2. 

Add: 

(1)      (2)    (3)     (4)     (5)     (6)     (7)     (8)  (9)  (10) 

95      39      53      23      85      99      29      82      55  59 

23      92      39      19      23      92      89      95      22  39 

59      15      99      51      99      29      22      23      92  92 

31      23      92      32      91      91      12      29      92  92 

92      52     29      95      22      12      55      59      23  25 

95  35  91  13  95  25  33  32  94  23 
23  93  12  21  13  53  12  92  10  59 
22  24  25  32  24  38  23  24  24  39 
59  68  51  48  58  64  57  56  57  54 
99988679989878987998 

Make  a  table,  subtracting  3  from  numbers  end- 
ing in  2 ;  from  numbers  ending  in  one. 
Make  problems  for  these  forms : 

32  -  3  =  29.  41  -  3  =  38. 

24.    6  +  3  and  3  +  6. 

(1)     (2)     (3)     (4)     (5)     (6)     (7)     (8)  (9)  (10) 

66  36  89  38  52  99  26  69  29  96 
33   83   22   99   31   21   63   92  62  29 

91  29  66  92  16  66  39  26  36  62 
26  92  33  26  63  33  92  63  93  36 
63  26  99  13  31  99  23  39  29  93 
39   63   29   69   96   22   36   92   32  29 

92  32  62  32  23  67  56  99  68  69 
26      93   36   96   32   36   27   23  27  36 

67  97   55   95   59   67   67   68   67  58 

96  88   99   78   79   99   90   89   67  98 


MISCELLANEOUS  PROBLEMS.  81 

25.     7  +  3   AND    3  +  7. 

Make  a  table,  adding  7  to  numbers  ending  in  3. 

Add: 

9,    9,    2,    3,    7,    2,    9,    9,    3,    7,    3,    6,    2,    9,   3,    7. 

6,    6,    7,    2,    9,    3,    7,    2,    9,    9,    3,    7,    2,    9,    9,    5. 

9,    7,    4,    3,    7,    2,    9,    9,    3,    6,    2,    9,    3,    7,    2,    9. 

8,   7,    5,    2,    9,    9,    3,    7,    3,    6,    2,    9,   3,    5,    2,    3,    7. 

3+7,    AND    REVIEW. 
(1)     (2)     (3)     (4)     (5)     (6)     (7)     (8)     (9)     (10) 


69 

99 

99 

92 

99 

62 

29 

96 

73 

78 

32 

79 

22 

26 

99 

36 

90 

73 

37 

32 

76 

32 

56 

73 

29 

73 

22 

39 

93 

97 

33 

96 

33 

39 

82 

30 

68 

19 

99 

93 

77 

24 

99 

99 

27 

99 

32 

92 

20 

29 

33 

97 

29 

22 

73 

9 

77 

97 

9 

72 

99 

73 

62 

63 

30 

92 

33 

23 

72 

36 

9 

32 

37 

38 

65 

23 

92 

57 

38 

95 

96 

89 

74 

79 

6 

98 

99 

7 

65 

98 

66 

69 

79 

80 

99  ■ 

■  69 

79 

96 

97 

70 

26.    MISCELLANEOUS  PROBLEMS. 

1.  A  man  paid  $72  for  a  wagon  and  $8  for  re- 
pairs, then  sold  it  at  a  loss  of  $9 ;  how  much  did 
he  receive  for  it  ? 

2.  Three  men  bought  a  horse  :  the  first  man 
paying  $36,  the  second  man  $15,  and  the  third 
man  as  much  as  the  first  two;  how  much  did 
the  horse  cost? 


6E 


82  ELEMENTARY  ARITHMETIC. 

3.  If  I  buy  11  yards  of  velvet  at  $3  a  yard; 
and  sell  it  at  $4  a  yard,  how  much  shall  I  gain  ? 

4.  If  a  boy  earns  $12  a  week  and  spends  $7, 
how  much  will  he  save  in  8  weeks  ? 

5.  Willie  gathered  a  bushel  of  chestnuts:  he 
giive  his  brother  10  quarts,  kept  6  quarts,  and 
sold  the  remainder;  how  many  quarts  did  he 
sell? 

6.  When  Alfred  reads  8  pages  more  he  will 
have  finished  his  story  book,  which  contains  90 
pages ;  how  many  pages  has  he  read  ? 

7.  A  man  gave  a  watch  and  $10  in  money  for 
a  horse  worth  $75 ;  what  is  the  value  of  the 
watch  ? 

8.  Two  persons  start  from  the  same  point  and 
travel  in  opposite  directions :  one  travels  26  miles 
and  the  other  38  miles  ;  how  far  apart  are  they  ? 

9.  A  man  saved  24  dollars  one  month,  half  as 
much  the  next  month,  and  6  dollars  the  third 
month ;  how  much  money  had  he  saved  at  the 
end  of  the  three  months  ? 

10.  If  82  feet  of  wire  are  already  used  in  mak- 
ing a  fence,  and  9  feet  more  are  needed,  how  much 
wire  will  be  used  ? 

11.  James  shoots  an  arrow  which  does  not  reach 
the  mark  by  9  feet.  If  the  mark  is  51  feet  away, 
how  far  is  the  arrow  from  James  ?     (Drawing.) 


ADDITION.  83 

27.     8  +  3    AND    3  +  8. 

Make  a  table,  adding  8  to  numbers  ending  in  3. 

Add: 

6,  7,  8,  2,  8,  9,  3,  8,  9,  3,  8,  9,  3,  8,  9. 
9,    9,  3,  9,  3,  8,  9,  2,  9,  9,  3,  8,  9,  0,  9. 

7,  4,  9,  3,  8,  9,  3,  8,  9,  2,  9,  9,  0,  3,  7. 
9,    8,  3,  3,  7,  3,  8,  9,  2,  9,  9,  3,  7,  3,  8. 


(1) 

(2) 

(3) 

<*) 

(o) 

(6) 

(<) 

(8) 

(9) 

(10) 

82 

30 

93 

89 

88 

59 

93 

7 

89 

90 

39 

99 

99 

32 

33 

32 

99 

87 

32 

23 

93 

8 

89 

76 

97 

99 

29 

33 

9 

69 

87 

83 

32 

33 

83 

98 

72 

79 

78 

8 

39 

37 

99 

7 

39 

23 

37 

28 

33 

33 

72 

93 

98 

93 

78 

97 

93 

82 

97 

79 

29 

99 

23 

89 

33 

83 

89 

32 

83 

33 

8 

23 

94 

38 

99 

36 

38 

93 

33 

99 

86 

59 

89 

65 

94 

57 

56 

88 

58 

89 

77 

99 

77 

88 

67 

97 

97 

88 

99 

80 

Add: 

(11)  99,  78,  33,  97,  93,  29,  98,  83,  38,  44,  and  98. 

(12)  88,  33,  99,  89,  32,  99,  92,  28,  98,  84,  and  69. 

Find  the  sum  of: 

(13)  93,  35,  33,  53,  94,  39,  43,  43,  77,  and  98. 

(14)  62  +  39  +  89  +  23  +  93  +  35  +  43  +  43  +  87  +  77  : 
what  ? 

28.    9  +  3  AND   3  +  9. 

3      13      23      33      43      53      63      73      83      93 
9999997999 


84  ELEMENTARY  ARITHMETIC. 


9 

19 

29 

39 

49 

59 

69 

79 

89 

99 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

Add: 

9,    4,  9,  8,  2,  9,  9,  3,  9,  8,  3,  8,  9,  9,  1. 

9,    9,  3,  9,  3,  9,  9,  9,  3,  9,  8,  3,  9,  9,  9. 

8,    5,  9,  9,  9,  3,  7,  3,  8,  9,  3,  9,  8,  0,  9. 

8,    9,  3,  3,  7,  3,  8,  9,  3,  9,  7,  2,  9,  9,  2. 

51  +  9=--?  62  +  7  =  ?  72-3=?  70-2  =  ? 

72  +  6=?  73  +  7=?  91-2=?  90-1  =  ? 

81  +  8=?  92  +  8  =  ?  81-3  =  ?  80-3=? 

83  +  9=?  83  +  5=?  32-3=?  91-3=? 

29.     3  +  9    AND    9  +  3,    AND    REVIEW. 

(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

99  99  89  99  89  99  90  8  88  97 

93  38  39  39  93  99  39  39  93  99 

30  93  93  79  39  39  99  83  99  33 

78  77  99  33  98  93  93  99  39  99 

99  30  98  99  93  89  29  39  99  89 

33  89  33  98  97  38  99  92  83  32 

9  93  9  93  33  93  82  89  37  86 

99  8  83  37  93  24  37  35  6  90 

96  33  99  54  98  67  55  86  57  6 

66  59  69  89  69  69  98  60  90  78 

Add: 

(11)  98,  89,  33,  79,  39,  80,  9,  92,  38,  98,  and  54. 

(12)  99,  20,  83,  97,  33,  99,  8,  83,  34,  78,  and  78. 

Find  the  sum  of: 

(13)  3,  35,  39,  53,  94,  34,  49,  43,  89,  and  79. 

(14)  95  +  39  +  33  +  45  +  83  +  39  +  63  +  34  +  97+67; 


what  ? 


UNITED   STATES  MONEY. 


85 


30.    UNITED   STATES    MONEY. 


Mir^e* 


Draw  the  one-cent  piece  upon  your  slate.  Draw 
the  dime.     How  many  cents  equal  a  dime  ? 

How  many  cents  make  a  dollar  ? 

How  many  tens  make  one  hundred  ?  How  many 
dimes  make  a  dollar  ?     One  dollar  is  written,  $1. 

10  cents   =  1  dime. 
10  dimes  =  $  1. 

Half  a  dollar  is  how  many  cents  ?  50  is  what 
part  of  100  ?     50  cents  is  what  part  of  $1  ? 

25  cents  are  what  part  of  100  cents?  What 
part  of  $1  ?  What  part  of  50  cents?  I  of  $1  is 
how  many  cents  ? 

1  of  $1  are  how  many  cents  ?  1  of  $1  is  how 
many  cents  ? 


86  ELEMENTARY  ARITHMETIC. 

I  of  $1  is  how  many  dimes?  \  of  $1  is 
how  many  dimes?  Half  a  dime  is  how  many 
cents  ? 

I  have  two  pieces  of  money  which  make  a  half- 
dime  ;  what  are  they  ? 

What  3  kinds  of  coins  can  you  select  to  make  a 
dime  in  value  ? 

If  I  spend  I  of  $1,  how  many  fourths  shall  I 
have  left  ?     How  many  cents  ? 

Find  with  the  counters  (buttons  or  button  molds) 
100  cents ;  find  5  more  cents.  How  many  cents 
have  you  ?     How  many  dollars  and  cents  ? 

To  show  that  we  have  one  dollar  and  five  cents, 
we  write  it  in  this  way:  $1.05,  placing  a  period 
between  dollars  and  cents. 

Write  one  dollar  and  three  cents ;  one  dollar 
and  six  cents. 

The  cents  are  written  at  the  right  of  the  dollars, 
with  a  period  beticeen  the  dollars  and  cents.  Two 
places  are  required  to  express  cents  when  the 
dollar  sign  is  used. 

31.  Begin  with  $1,  and  write  all  the  dollars 
and  cents  up  to  $1.25. 

Write  the  following  in  figures  : 

One  dollar  fifty  cents ;  one  dollar  and  sixty-nine 
cents ;  one  dollar  one  cent ;  one  dollar  and  ninety- 
nine  cents 


UNITED  STATES  MONEY.  87 

Read  the  following : 

(1)  (2)  (3)      '        (4)  (5) 

$0.06  $1.02  $1.10  $1.70  $0.03 

$1.00  $1.09  $1.01  $1.71  $1.44 

$1.07  $1.90  $1.75  $1.17  $1.50 

$1.88  $1.17  $0.98  $1.27  $1.80 

$1.11  $1.60  $1.36  $1.05  $1.08 

Write  the  above  numbers  and  add. 

Add  as  in  simple  numbers,  and  separate  dollars  from  cents  by  a  period. 

How  many  cents  in  $2  ?     In  $3  ?     In  $4  ? 

Write  the  following  in  figures : 

Two  dollars  seven  cents;  two  dollars  twelve 
cents ;  three  dollars  forty  cents ;  four  dollars 
ninety  cents  ;  five  dollars  nine  cents ;  seven  dol- 
lars seven  cents. 

32.    Read  the  following : 

$6.08  $0.01  $5.05  $6.15  $7.71  $20.05 

$9.10  $8.01  $4.01  $6.51  $7.07  $30.50 

$7.05  $9.09  $3.10  $0.05  $10.50  $29.16 

$4.04  $5.50  $6.11  $7.17  $10.05  $40.12 

How  many  cents  in  two  dollars  ninety-five 
cents  ? 

How  many  dollars  in  six  hundred  fifty  cents  ? 

How  many  hundreds  in  seven  hundred  ninety  ? 

How  many  50's  in  200  ? 

How  many  50-cent  pieces  in  $2. 

Put  down  a  dollar  for  each  hundred  cents  in 
ten  dollars.  How  many  hundred  cents  make  ten 
dollars  % 


88  ELEMENTARY  ARITHMETIC. 

How  many  cents  make  seven  dollars  seven 
cents  ? 

1.  Find  the  sum  of  $9.06  and  $12.20. 

2.  Find  the  sum  of  $15.25  and  $4.30. 

3.  $12.00—    $5.00.  5.    $20.00  —  $6.00. 

4.  $15.50  -  $12.50.  6.     $9.30  —  $8.30. 

33.     MISCELLANEOUS  PROBLEMS. 

1.  A  boy  earned  $1.65,  and  his  father  gave  him 
35  cents ;  he  paid  50  cents  for  a  scrapbook,  and 
50  cents  for  pictures  ;  how  much  money  had  he 
left? 

2.  Bought  10  yards  of  cloth  at  4  dollars  a  yard, 
and  lost  $8  in  selling  it ;  how  much  did  I  get 
for  it? 

3.  A  boy  earned  75  cents  a  day,  and  paid  50 
cents  a  day  for  his  board ;  how  much  had  he  left 
at  the  end  of  6  days  ? 

4.  Max  has  a  quarter  of  a  dollar,  a  dime,  a 
3-cent  piece,  and  a  2-cent  piece;  how  much 
money  has  he  ?  James  has  \  as  much  money  as 
Max  ;    how  much  has  he  ? 

5.  We  paid  for  a  Christmas  tree,  $2 ;  for  tapers, 
40  cents;  for  candy,  75  cents;  for  netting  for 
candy  bags,  10  cents;  for  toys,  $1.20;  for  books, 
$3.60  ;    what  did  all  cost  ? 

6.  How  many  yards  of  fringe  will  be  needed  for 
a  rug  5  ft.  long  and  3  ft.  wide  ?     (Drawing.) 


REVIEW. 


89 


7.  A  class  of  children  made  69  holly  wreaths  to 
trim  a  schoolroom,  and  used  all  but  3  ;  how  many 
did  they  use  ? 

8.  If  i  of  a  yard  of  ribbon  costs  2  cents,  how 
many  yards  can  I  buy  for  32  cents? 

9.  A  man  bought  3  dozen  boxes  of  peaches,  but 
found  ia  of  them  unsound  ;  how  many  boxes  were 
sound  ? 

10.  Mary's  aunt  gave  her  a  doll  for  which  she 
paid  $4  ;  for  the  doll's  house  she  bought  a  set  of 
chairs  for  which  she  paid  $1.50,  a  sofa  for  $1,  a 
bedstead  for  $1.20,  and  a  little  bureau  for  90 
cents  ;    what  did  all  cost  ? 

11.  How  many  feet  must  a  boy  walk  in  going 
around  this  lot  ? 


64  ft 


d 

£ 

8 

34. 

REVIEW. 

p 

(1) 

(2) 

(3) 

W 

(5) 

(6) 

(7) 

(8) 

93 

62 

22 

99 

96 

69 

93 

33 

35 

39 

49 

29 

33 

29 

33 

33 

33 

89 

39 

63 

39 

32 

34 

45 

53 

23 

28 

35 

52 

56 

53 

99 

94 

93 

33 

93 

96 

93 

92 

23 

39 

35 

39 

39 

33 

39 

35 

64 

43 

43 

32 

42 

49 

43 

49 

34 

43 

43 

93 

43 

43 

43 

43 

93 

77 

87 

87 

88 

89 

87 

99 

98 

98 

77 

79 

78 

79 

78 

69 

79 

90  ELEMENTARY  ARITHMETIC. 

(9)       (10)      (11)      (12)      (13)      (14)      (15)      (16) 
89        29        93        26        97        32        23        23 


79 

63 

94 

33 

29 

96 

64 

56 

38 

34 

34 

68 

63 

23 

94 

39 

93 

84 

68 

89 

35 

39 

29 

23 

37 

28 

22 

21 

93 

63 

63 

65 

43 

92 

99 

99 

29 

25 

35 

23 

43 

89 

83 

83 

62 

43 

93 

83 

93 

33 

33 

33 

33 

43 

38 

23 

98 

79 

87 

89 

88 

99 

76 

87 

76 

79 

78 

76 

78 

68 

66 

87 

(17) 

(18) 

(19) 

(20) 

(21) 

(22) 

(23) 

(24) 

73 

62 

36 

98 

29 

82 

98 

96 

26 

26 

68 

32 

39 

99 

99 

99 

29 

53 

92 

39 

62 

39 

39 

33 

63 

37 

39 

58 

72 

42 

42 

65 

95 

93 

43 

93 

34 

49 

49 

23 

23 

39 

45 

39 

94 

99 

78 

89 

62 

42 

83 

42 

89 

83 

33 

22 

34 

41 

28 

43 

33 

33 

93 

93 

95 

89 

98 

77 

79 

79 

88 

97 

79 

79 

64 

79 

79 

76 

79 

79 

35.    SUBTRACTION. 

Subtract  2  and  3  from  numbers  ending  in  any 
one  of  the  digits.  Give  the  ending  figure  of  each 
result  first,  then  the  whole  remainder. 

(1)  11      12     23     34     45      56      67      78      89     91 

2222222222 

(2)  10     21     32      43      54     65     76      87      98      99 

33       3       3333333 


SUBTRACTION.  91 

(3)    21     42     51     43     61     72     81     62     91      101 
^2       3       2       3       3       3       2       3       2         3 

160  -  3  ?         (60  -  3  =  57.     160  -  3  =  157.) 
161  -  42  =  ? 
42  names  the  part  of  161  which  we  wish  to  take  out  of 
that  number. 

Write  ones  under  ones,  tens  under  tens.      (Place  the  bun- 
dles of  sticks,  1  hundred,   6  tens,  1  one,  over 
5  10         the  figures  161.) 
1    p   1  Subtract  ones  first.     2  ones  cannot  be  taken 

g   jj  out    of   1    one.       Take    1  ten    from    the    tens, 

119  leaving  5  tens.     (Show  with  the  sticks.) 

The  1  ten  which  we  have  taken  is  equal  to 
10  ones,  which  we  add  to  the  1  one  to  make  11  ones.  2  ones 
from  11  ones  leaves  9  ones,  which  is  written  in  ones' 
place  below  the  line.  4  tens  from  5  tens  leaves  1  ten, 
which  is  written  in  tens'  place  below  the  line.  No  hun- 
dreds from  1  hundred  leaves  1  hundred. 

119  is  the  part  of  161  which  we  wished  to  find.  The 
two  parts  make  what  number  ? 

Taking  a  part  of  a  number  out  of  it,  to  find  the  remainder 
is  called  Subtraction. 

The  number  to  be  diminished  by  taking  one  of  the  parts 
is  called  the  Minuend. 

The  part  taken  out  of  the  minuend  is  called  the  Subtra* 
hend :  the  part  left  is  called  the  Remainder. 

The  sign  of  Subtraction  ( — )  is  called  minus  or  less. 
14  —  6  =  8,  is  read,  14  minus  6  equals  8  :  it  means  that  14 
made  6  less  is  equal  to  8. 


36. 

Subtract : 

(i) 

(2)   (3) 

(4) 

(5) 

(6) 

(?) 

(8) 

160 

251   261 

252 

252 

263 

141 

230 

42 

22    32 

33 

42 

34 

22 

24 

(9)   (10)   (11)   (12)   (13)   (14)   (15)   (16) 

231   130   241   142   240   331   212   161 

23    22    23    33    22    14    34    33 


92  ELEMENTARY  ARITHMETIC. 

(17)  (18)  (19)  (20) 

184-45=?  153-35=?  174-146  =  ?  183-156  =  ? 

(21)  (22)  (23)  (24) 

168  -  59  =  ?  173  -  49  =  ?  163  - 138  =  ?  177  - 148  =  ? 

(25)  (26)  (27)  (28) 

140-23  =  ?  165-48  =  ?  192-147  =  ?  190-137  =  ? 

(29)  (30)  (31)  (32) 

156-39  =  ?  182-55  =  ?  180-168  =  ?  180-146=? 

(33)  (34)  (35)  (36) 

191_44-?  194-58  =  ?  162-136=?  161-138  =  ? 

(37)  (38)  (39)  (40) 

165-59  =  ?  161-45  =  ?  183-157  =  ?  190-129  =  ? 

(41)  (42)  (43)  (44) 

140-24  =  ?  162-39  =  ?  192-168  =  ?  187-158  =  ? 

(45)  (46)  (47)  (48) 

181-67  =  ?  191-69  =  ?  171-136  =  ?  188-179  =  ? 

(49)  (50)  (51)  (52) 

194-69  =  ?  180-45  =  ?  195-147=?  135-  48  =  ? 

(53)   (54)   (55)   (56)  (57)   (58)   (59)   (60)   (61) 

164  125  130  120  191  128  191  106.  104 
58   36   39   49   83   69   94   37   59 

37.     MISCELLANEOUS    PROBLEMS. 

1.  Two  persons  start  from  the  same  place  and 
travel  in  the  same  direction ;  one  travels  40  miles 
an  hour,  and  the  other  35  miles  an  hour ;  how- 
far  apart  will  they  be  in  1  hour?  (Show  by 
drawing.)     How  far  in  6  hours? 

2.  Charles  gets  $6  a  month  for  selling  a  daily 
paper ;  Henry  gets  \  as  much  for  selling  a  weekly 
paper ;  how  much  will  both  have  earned  .  in  5 
months  ? 

3.  From  a  chest  of  tea,  containing  60  pounds, 
9  pounds  were  sold  at  $1  a  pound ;  what  was  the 
value  of  the  remainder,  at  the  same  rate  ? 


MISCELLANEOUS   PROBLEMS.  93 

4.  I  bought  a  bushel  of  tomatoes  for  70  cents, 
a  half-bushel  of  turnips  for  20  cents,  and  a  peck 
of  beans  for  10  cents;  what  I  paid  for  all  was  8 
cents  more  than  the  cost  of  half  a  bushel  of  sweet 
potatoes.     What  did  the  sweet  potatoes  cost  ? 

5.  A  box  contains  134  oranges,  and  a  barrel 
contains  64  more  than  the  box  ;  how  many 
oranges  in  the  barrel? 

6.  I  bought  a  horse  and  sleigh  for  $150;  the 
sleigh  cost  $45  ;  what  did  the  horse  cost  ? 

7.  After  spending  $80  for  a  pony,  George 
found  that  he  had  $65  left  in  his  savings  bank; 
how  much  money  had  he  at  first  ? 

8.  In  an  orchard  there  are  150  apple  trees; 
this  is  50  more  than  the  number  of  peach  trees; 
how  many  peach  trees  are  there  ? 

9.  A  man  having  190  young  orange  trees, 
bought  89  more,  and  then  sold  50 ;  how  many 
had  he  left  ? 

10.  Add  three  hundred  nine  to  seven  hundred 
-eleven,  and  subtract  twenty-nine. 

11.  A  farmer  bought  40  sheep  for  144  dollars 
at  one  time,  and  50  sheep  for  155  dollars  at  another 
time  ;   how  much  did  the  sheep  cost  him  ? 

12.  A  boy  shot  an  arrow  145  feet  up  the  road, 
and  another  149  feet  down  the  road ;  how  far 
were  the  arrows  apart  ?     (Drawing.) 


94  ELEMENTARY  ARITHMETIC. 

38.    READING  AND  WRITING   NUMBERS. 
HOW   TO    EXPRESS    THOUSANDS. 

You  have  learned  that  the  number  one  thousand 
is  expressed  by  writing  the  figure  1  to  the  left  of 
hundreds. 

Read  the  following  numbers  : 

1,500       1,230       1,400       1,670        1,873        1,999 
1,220       1,864       1,748        1,976        1,449        1,650 

The  period  of  ones  is  separated  from  the  thou- 
sands by  a  comma. 

Write  in  figures :  two  thousand,  three  thousand, 
five  thousand,  eight  thousand,  nine  thousand. 

Read  the  following  numbers : 


(1) 

(2) 

(3) 

(4) 

(5) 

3,000 

7,000 

6,350 

4,500 

9,400 

3,200 

5,102 

8,008 

1,111 

0,444 

4,340 

2,501 

8,108 

1,001 

2,020 

8,650 

7,206 

0,888 

1,100 

4,009 

9,241 

7,777 

5,230 

1,004 

9,999 

39.   The  greatest  number  that  can  be  expressed 
by  four  figures  is  9,999. 
Write  in  figures  : 

Three  thousand  seven  hundred  fifty. 
Eight  thousand  two  hundred  two. 
One  thousand  eleven ;  one  thousand  one. 
Five  thousand  five ;  five  thousand  fifty. 
Four  thousand  thirty-five ;  four  thousand  five. 


TABLE   OF  ROMAN    NOTATION. 


95 


Express  in  figures  numbers  composed  of : 

0  thousands  6  hundreds  7  tens  and  4  ones. 


3 

u 

3 

a 

3 

u 

"  3   " 

9 

u 

8 

u 

5 

u 

"  6  " 

8 

a 

0 

a 

0 

a 

a     j      t( 

5 

it 

9 

a 

9 

u 

"  0  " 

40. 

TABLE  OF 

ROMAN 

NOTATION. 

30 

40 

50 

60 

70 

80     90 

100 

XXX 

XL 

L 

LX 

LXX 

LXXX    XC 

C 

When  a  letter  is  repeated,  its  value  is  repeated. 

When  a  letter  is  placed  after  one  of  greater 
value,  its  value  is  added;  when  placed  before, 
its  value  is  subtracted  from  the  greater. 

Express  the  following  numbers  by  figures: 


XXXIX  LIX 

XLIX  LXV 

XLVIII  LXX 

XIX  XLXXX 


XC  XCIX 

XCI  XCVIII 

LXXXIX  LXXIX 

XCVIII  XLIV 


XXIX 


LXXX        LXXXVIII 


LXVI 


41. 

REVIEW. 

Copy 

and  add  : 

(1) 

(2) 

(3) 

W 

(^ 

(6) 

393 

995 

767 

933 

762 

739 

335 

239 

799 

373 

985 

833 

539 

633 

333 

483 

333 

959 

853 

345 

854 

423 

469 

393 

994 

983 

234 

893 

433 

933 

334 

339 

928 

233 

824 

345 

949 

463 

843 

943 

244 

449 

343 

434 

343 

343 

943 

483 

389 

897 

788 

387 

888 

799 

979 

767 

878 

997 

879 

779 

96  ELEMENTARY  ARITHMETIC. 


(?) 

(8) 

(9) 

(10) 

(11) 

(12) 

388 

399 

899 

188 

929 

385 

339 

338 

993 

998 

399 

633 

583 

593 

339 

939 

533 

863 

994 

999 

348 

293 

337 

233 

334 

329 

343 

999 

953 

994 

438 

432 

498 

828 

999 

888 

433 

432 

983 

393 

283 

333 

843 

842 

333 

333 

333 

383 

987 

977 

379 

338 

376 

398 

779 

779 

977 

799 

779 

798 

42. 


MISCELLANEOUS    PROBLEMS. 


1.  John  had  11  quarts  of  nuts  and  sold  8  pints ; 
how  many  had  he  left  ? 

2.  A  girl  sold  3  quarts  of  berries  each  day  for 
10  days  ;  how  many  pecks  did  she  sell  ? 

3.  A  druggist  has  7  gal.  2  qt.  of  kerosene.  How 
long  will  it  last  him  if  he  sells  1  quart  each  day  ? 

4.  A  carpenter  bought  a  piece  of  wood  4  ft.  6 
in.  long,  at  8  cents  a  foot ;  what  did  the  wood  cost 
him? 

5.  How  many  sashes,  each  3  yd.  1  ft.  long,  can 
be  cut  from  10  yd.  of  silk  ? 

6.  How  many  pint  bottles  will  it  take  to  hold 
3  gallons  of  ammonia  ? 

7.  If  you  pick  4  pecks  of  berries  a  day,  and  I 
pick  2  pecks,  in  how  many  days  will  we  pick  6 
bushels  ? 


MISCELLANEOUS  PROBLEMS.  97 

8.  A  merchant  living  18  miles  out  of  Chicago, 
goes  to  the  city  every  morning  and  returns  in 
the  evening ;  how  many  miles  does  he  travel  in 
4  days? 

9.  A  shoe  merchant  sold  four  dozen  pairs  of 
shoes  for  $192;  this  is  $24  more  than  they  cost 
him  ;   what  did  they  cost  ? 

10.  Holt  &  Co.  sold  620  pairs  of  gloves  this 
month,  which  is  20  pairs  less  than  they  sold  last 
month ;  how  many  pairs  were  sold  last  month  ? 

43.    Subtract  : 

(1)           (2)           (3)  (4)  (5)  (6) 

4221    5121  7011  3121  6321  4112 

132    223    213  232  332    123 


7. 

9131- 

322  =  ? 

13.  2121-312 

==? 

19.  5012 

-  223  =  ? 

8. 

4011- 

303  =  ? 

14.  4118-223 

=  ? 

20.  4610 

-  132  =  ? 

9. 

5210- 

223  =  ? 

15.  5102-213 

— .? 

21.  7051 

-  233  =  ? 

10. 

3101- 

222  =  ? 

16.  6110-123 

=  ? 

22.  6311 

-  233  =  ? 

11. 

5119- 

223  =  ? 

17.  8112.-213 

=  ? 

23.  5012 

-  213  =  ? 

12. 

3122- 

123  =  ? 

18.  7231-322 

=  ? 

24.  6300 

-1311 

.  =  ? 

44.  Add: 

(1) 

(2) 

(3) 

w 

(5) 

W 

(?) 

(8) 

(9) 

329 

782 

973 

66S 

993 

388 

922 

725 

296 

563 

999 

992 

382 

369 

29 

225 

963 

927 

335 

393 

235 

829 

632 

878 

763 

273 

263 

883 

425 

953 

293 

25S 

133 

197 

723 

539 

223 

483 

339 

935 

939 

393 

333 

224 

333 

993 

823 

588 

353 

382 

683 

548 

369 

834 

884 

283 

323 

433 

429 

134 

341 

322 

244 

338 

925 

393 

433 

493 

395 

933 

433 

325 

796 

894 

399 

937 

999 

497 

939 

969 

469 

766 

775 

878 

697 

569 

778 

799 

787 

976 

IE 


98  ELEMENTARY  ARITHMETIC. 

(10)      (11)      (12)       (13)      (14)      (15)      (16)      (17)      (18) 


997 

893 

97 

776 

338 

686 

998 

737 

695 

393 

95 

93 

983 

539 

838 

239 

939 

333 

438 

939 

929 

334 

363 

262 

893 

363 

343 

342 

258 

388 

533 

899 

939 

289 

484 

443 

749 

933 

523 

368 

233 

388 

233 

434 

884 

382 

389 

399 

882 

945 

533 

434 

878 

228 

922 

422 

982 

299 

343 

393 

434 

923 

983 

393 

493 

333 

933 

888 

393 

343 

393 

323 

397 

98 

377 

889 

896 

399 

379 

789 

398 

977 

778 

879 

779 

676 

775 

878 

787 

978 

45.     MISCELLANEOUS   PROBLEMS. 

1.  James  has  9  cents,  John  three  times  as  many 
less  6 ;  how  many  has  John  ?  How  many  have 
both? 

2.  One  day  a  man  traveled  25  miles  by  rail- 
road, 34  miles  by  steamboat,  and  19  miles  by 
stage,  and  returned  18  miles ;  how  far  is  he  from 
home? 

3.  I  bought  4  yards  of  silk  at  $2  a  yard,  2 
shawls  at  $10  each,  and  some  cashmere  for  $10; 
how  much  change  ought  I  to  receive  from  4  ten- 
dollar  bills  ? 

4.  A  grocer  paid  $165  for  30  barrels  of  flour. 
$50  for  100  barrels  of  potatoes,  and  $45  for  15 
barrels  of  apples  ;  how  much  did  he  pay  for  all  ? 

5.  A  boy  who  had  53  marbles  loaned  20,  and 
afterwards  borrowed  9  more ;  how  many  marbles 
had  he  then  ? 


MISCELLANEOUS  PROBLEMS.  99 

6.  A  boy  paid  $20  for  a  team  of  goats,  $8  for 
his  carriage,  and  $4  for  harness ;  he  sold  them  for 
1  less  than  they  cost  him ;  for  how  much  did  he 
sell  them  ? 

7.  I  bought  3  yards  of  cloth  at  $7  a  yard  for  a 
coat ;  the  buttons  and  cord  cost  $2,  the  making 
of  it  $6  ;  for  how  much  must  I  sell  it  to  gain 
$5.50  ? 

8.  A  pole  is  40  feet  long.  If  1  of  it  is  in  the 
ground,  ^  of  it  in  the  water,  and  the  rest  in  the 
air,  how  many  feet  in  the  air  ? 

9.  A  man  gave  a  carriage  and  $100  in  money 
for  a  lot  worth  $400  ;  what  was  the  value  of  the 
carriage  ? 

10.  Some  children  returned  from  the  lake  with 
a  basket  of  shells ;  after  giving  half  of  them  away 
they  had  95  left;  how  many  had  they  at  first? 

11.  A  party  of  school  children  went  to  Fair- 
view  Park:  $1.75  is  50  cents  less  than  they  paid 
for  car  fare  ;  how  much  did  they  pay  ? 

12.  John  bought  a  pack  of  shingles,  and  after 
mending  the  roof  had  75  left;  if  he  used  175,  how 
many  did  the  pack  contain  at  first  ? 

13.  A  farmer  having  $157  paid  one  half  of  his 
money  for  a  horse,  and  one  half  the  remainder  for 
a  cow ;  how  much  did  each  animal  cost,  and  how 
much  money  had  he  left  ? 


100  ELEMENTARY  ARITHMETIC. 


CHAPTER    IV. 

NUMBERS   FROM    FORTY   TO    FIFTY. 

1.  Draw  42  leaves  and  divide  them  into  sevens. 
7  can  be  taken  out  of  42  how  many  times  ? 

42  -^  7  =  ?  6x7  =  ?  J  of  42  =  ? 

If  you  have  42  pansies,  tied  in  bunches  of  7 
each,  how  many  bunches  will  you  have  ? 

Draw  the  leaves  in  sixes.  42  equals  how  many 
6's  ?    42  -  6  =  ?     7x6  =  ?    |  of  42  =  ? 

How  many  days  in  6  weeks  ? 

Plant  42  tuberoses  in  7  equal  rows ;  how  many 
in  each  row  ?     (Drawing.) 

Make  questions  for : 
7  x  6  as  42.  42  -f-  7  =  6.  \  of  42  =  6. 

42  equals  how  many  4's  ?  How  many  8's  ? 
How  many  5*8  ? 

A  family  used  42  bushels  of  apples  in  8  months; 
at  that  rate,  how  many  bushels  were  used  in  one 
month  ? 

2.  Draw  44  circles  in  fours. 

44^4  =  ?  11x4  =  ?  Ti,-of44  =  ? 


NUMBERS  FROM  FORTY  TO  'FlI^Y.  101 

At  a  picnic  44  cups  of  lemondde.^vere  .passed  to' 
11  rows  of  children;  how  many  ciipd* were'  p&&se$  •/,' 
to  each  row  ? 

Divide  44  into  elevens. 
44  +- 11  =  ?  4  x  11  =  ?  i  of  44  =  ? 

44  quarts  of  ice-cream  are  how  many  gallons  ? 

3.    review. 


6  x    7    =  ?    44 


4  x  10i  =  ?    42 
8  x    5J  =  ?     42 


11  s  ?     J  of  42  =  ?      8x5%  =  ? 


11  X    4    5=  ?     43  -T- 10  =  ?     J  of  41  =  ?     41-5    =  ? 


7  =  ?     £of42  =  ?    42 -f- 6    =  ? 

8  =  ?     £  of  43  =  ?       6  X  7£  =  ? 


John  gathered  42  quarts  of  chestnuts ;  how 
many  pecks  did  he  gather  ? 

Mary  goes  to  school  44  weeks  in  the  year;  if 
there  are  4  terms  of  equal  length,  how  many 
weeks  in  each  term  ? 

How  long  will  43  pounds  of  butter  last,  if  used 
at  the  rate  of  6  pounds  a  week  ? 

43  pecks  of  apples  are  how  many  bushels  ? 

At  $5  a  pair,  how  many  pairs  of  shoes  can  be 
bought  for  $43  ? 

Make  problems  for  : 

.    6  X  7  =  42.  7  X  6  =  42.  J  of  41  =  10J. 

J  of  41  =  8*.         i  of  42  =  51  43  -T-  4  =  10  J. 

4.  Draw  45  wheels  in  nines.  45  equals  how 
many  nines  ? 

45  -r-  9  =  ?     5x9  =  ?     J  of  45  =  ?     §of45  =  ? 


••102        \  .**  XfrbitENTARY  ARITHMETIC. 
•  I  •    •  ••    *,  «'  •    « « 

:  •. 

. :  .:At;9».*(5^ts:.avpoirnd?  how  many  pounds  of  raisins 
'  bari  you  get  for  45  cents  ? 

Draw  45  wheels  in  5's.  45  equals  how  many 
5's? 

45  -f-  5  =  ?        9x5  =  ?        J  of  45  =  ? 

How  many  yards  in  9  rolls  of  wall  paper,  if  each 
roll  contains  5  yards  ? 

J  of  45  =  ?         J.  of  45  =  ? 

5.  Draw  48  spools  in  12's.  48  equals  how 
many  12's  ? 

48  -  12  =  ?  4  x  12  =  ?  12  is  what  part  of 
48?    |  of  48  =  ? 

48  inches  of  ribbon  will  make  how  many  neck- 
ties, if  12  inches  make  one  neck-tie  ? 

At  12  cents  a  dozen,  what  will  4  dozen  buttons 
cost? 

48  equals  how  many  4's  ?     48  4-  4  =  ?     12  x  4  =  ? 

4  is  what  part  of  48  ? 

At  4  cents  each,  how  many  papers  of  needles 
can  be  bought  for  48  cents  ? 

How  many  tires  have  the  wheels  of  4  wagons  ? 

Ella  drew  48  beech  nuts,  8  in  each  group  ;  how 
many  8's  did  bhe  draw  ?     48  is  how  many  8Js  ? 

48-8  =  ?  6x8  =  ?  |  of  48  =  ?  8  roses  is  I 
of  all  the  roses  I  gathered  this  morning ;  how 
many  did  I  gather  ? 

48  is  how  many  6*8  ?     48  -f-  6  =  ?     8x6  =  ? 


NUMBERS  FROM  FORTY  TO  FIFTY.  103 

6  is  |  of  the  number  of  children  iii  school ;  how 
many  are  there  in  school  ? 

I  paid  6  cents  for  a  stamp  for  a  package ;  how 
many  such  stamps  will  48  cents  buy  ? 

6.  49  is  how  many  7's  ?  49  -5-  7  =  ?  7x7  =  ? 
\  of  49  =  ? 

49  loaves  of  bread  will  last  a  camping  party  how 
many  days,  if  they  use  7  loaves  a  day  ? 

Make  problems  for  : 

tV  of  49  =  4^.      J  of  49  =  12|. 

7.  50  equals  how  many  10's  ?  50  -f-  10  =  f 
5x10  =  ?     £of50  =  ? 

Five  pairs  of  gloves  have  how  many  fingers  ? 

50  equals  how  many  4's  ?  50  bushels  of  apples 
are  how  many  pecks  ?  Divide  50  sheets  of  drawing 
paper  equally  among  4  pupils ;  how  many  sheets 
will  each  receive  ? 

50  equals  how  many  12's  ?     4  x  12|  =  ? 

At  121  cents  a  yard,  how  many  yards  of  muslin 
can  be  bought  for  50  cents  ? 

50  equals  how  many  6's  ?  81  sixes  are  how 
many  ?     J  of  50  =  ?     8§  id  what  part  of  50  ? 

At  6  cents  a  yard,  how  many  yards  of  ribbon 
can  you  buy  for  50  cents  ? 

50  equals  how  many  8's  ?  6|  eights  are  how 
many  ones  ?  6i  is  what  part  of  50  ?  6|  times  8 
equals  what  ?     \  of  50  =  ? 


104  ELEMENTARY  ARITHMETIC. 

'•'I  gave   50  cents  for   8  yards  of   calico;   how 
i/ijJiE/iS:  th#t>**a  yard  ? 
Make  problems  for : 

6  X  8£  =  50.       50  -s-  6  =  8J.       50  -f-  8  =  6J. 

8.    REVIEW. 

48  -f-  12  =  ?       \  of  50  =  ?       6  x    8J  =  ?  8  X    6 J  =  ? 

49  -T- 12  =  ?       £  of  48  =  ?       4  X  12J  =  ?  12  x    4   =  ? 

50  -r- 12  =  ?       |  of  49  =  ?       7x7=?  4  x  12  J  =  ? 
48-7-6  =  ?       J  of  48  =  ?       6x8=?  8x6=? 

50  cents  is  how  many  5-cent  pieces  ?  How 
many  dimes  ? 

How  many  2-cent  postage  stamps  can  you  buy 
for  50  cents? 

If  you  can  get  2  oranges  for  5  cents,  how  many 
can  you  get  for  50  cents  ? 

When  eggs  are  8|  cents  a  dozen,  how  many  dozen 
can  be  bought  for  50  cents  ? 

A  pole  48  feet  long  is  i  in  the  water  and  f  in  the 
air.     How  many  feet  are  in  the  air  ? 

At  6|  cents  a  ball,  how  many  balls  of  twine  can 
you  buy  for  50  cents  ? 

Make  problems  for : 

*  of  49  =  7.  7x7  =  49.  i  of  49  =  12J. 

6)48  4)50 

8  12* 

8  x  6J  =  50.  12  x  4£  =  50.  6  x  8$  =  50. 


NUMBERS  FROM  FORTY  TO  FIFTY. 


105 


9-   Copy 

and  learn  : 

42  ~   7=   6. 

6x7  =  ? 

48 -r-   4  =  12. 

12  x    4  =  ? 

42- 

-6=7. 

7x6  =  ? 

48-    8=    6. 

6x8  =  ? 

44- 

-11=   4. 

4  x  11  =  ? 

48 -^    6=    8. 

8x6  =  ? 

44- 

-   4=11. 

11  X    4  =  ? 

49^-    7=    7. 

7x7  =  ? 

45- 

-9=5. 

5x9  =  ? 

50-^10  =    5. 

5  x  10  =  ? 

45- 

-5=9. 

9X5  =  ? 

50^   5=10. 

10  x    5  =  ? 

48- 

-12=   4. 

4  x  12  =  ? 

|  of  49  =  ? 

i  of  48  =  ? 

REVIEW. 

7x3=? 

27- 

-    9=  ? 

2  x  16  =  ? 

36  -f-  9  =  ? 

2  x  11  =  ? 

28- 

-    2=  ? 

4  x    8  =  ? 

35  -*-  5  =  ? 

3x8=? 

30- 

-15=  ? 

3  x  11  =  ? 

40  4-  8  =  ? 

9x3=? 

30- 

-    5=  ? 

7x5=? 

32  -i.  4  =  ? 

6x 

5=  ? 

28- 

-    7=  ? 

3  x  12  =  ? 

24  -f-  8  =  ? 

10.    A  pound  is  how  many  ounces  ?      Half  a 
pound  of  candy  is  how  many  ounces  ? 


If  I  put  the  pound  weight  on  one  side  of  the 
scales,  how  many  ounces  must  I  put  on  the  other 
side  to  balance  it  ? 


106  ELEMENTARY  ARITHMETIC. 

i  of  a  pound  is  how  many  ounces  ?  If  I  wish  to 
buy  a  quarter  of  a  pound  of  tea,  how  many  ounces 
must  be  put  upon  the  scales  to  balance  it  ? 

4  ounces  of  ginger  are  what  part  of  a  pound  ? 
At  5  cents  an  ounce,  what  will  \  of  a  pound  of 
celery  seed  cost? 

At  2  ounces  for  5  cents,  how  many  ounces  of 
pepper  can  be  bought  for  20  cents  ? 

1^  pounds  of  figs  are  how  many  ounces  ? 

|  of  a  pound  of  maple  sugar  is  how  many  ounces  ? 

16  ounces  (oz.)  are  1  pound  (lb). 
11.    Comparison  of  one  third  and  one  fifth  : 


Into  how  many  equal  parts  is  the  first  circle 
divided  ?  Into  how  many  equal  parts  is  the  second 
divided  ?     Which  is  more,  \  of  a  pie,  or  \  ? 

Into  how  many  equal  parts  is  the  third  circle 
divided?  What  is  one  of  the  fifteen  equal  parts 
called  ?  How  many  of  these  fifteenths  make  \  of 
the  whole  circle  ? 

1  is  how  many  fifteenths  ?  §  are  how  many 
fifteenths?     |  are  how  many  fifteenths? 

12.    Draw  the  second   circle  upon  your  slate; 


REVIEW.  107 

divide  it  into  fifths  by  strong  lines.  Divide  each 
fifth  into  three  equal  parts.  Into  how  many  parts 
is  the  whole  circle  now  divided  ? 

I  is  how  many  fifteenths  ?  §  are  how  many 
fifteenths  ? 

Look  at  the  third  circle  :  find  1  of  it.  Find  I  of 
the  whole  circle.     \  is  how  much  more  than  \  ? 

\  and  I  are  how  many  fifteenths  ?  §  and  §  are 
how  many  fifteenths  ? 

Robert  eats  |  of  a  melon,  gives  George  |?  and  the 
remainder  to  Harry ;  what  part  of  the  whole 
melon  does  Harry  get  ? 

13.  Look  at  the  circles,  and  answer  these 
questions : 

ft  are  how  many  thirds  ?  f  are  how  many  wholes  ? 

{%  are  how  many  thirds  ?  §  are  how  many  wholes  ? 

ft  are  how  many  fifths  ?  J^-  are  how  many  wholes  ? 

ft  are  how  many  fifths  ?  ^°-  are  how  many  wholes  ? 

f  J  are  how  many  wholes  ? 

3xf  =  ?      3  x |  =  ?      6  X  §  =  ?      6x|  =  ?      3xft  =  ? 

§  of  |  is  what  part  of  the  whole  ?     |  of  1  =  ? 

3     OI     15  —    i 

A  grocer  sold  §  of  a  box  of  tea,  and  used  I ; 
what  part  of  the  whole  remained  unsold  ? 


108  ELEMENTARY  ARITHMETIC. 

MEASURING   TIME. 


14.  Are  there  any  other  ways  of  measuring 
time  than  by  the  clock  and  the  hourglass  ?  Have 
you  ever  seen  a  sundial  ?  Which  one  of  the  kings 
of  England  is  said  to  have  measured  the  day  by 
burning  notched  candles  ? 

How  many  minutes  is  the  long  hand  in  passing 
from  one  figure  to  another  ? 

The  space  between  the  figures  is  divided  into 
five  equal  parts.  The  long  hand  is  a  minute  in 
passing  over  one  of  these  smallest  spaces.  See 
how  many  times  you  can  walk  across  the  floor  in 
a  minute.  Sit  still  and  watch  the  clock  a  minute ; 
notice  how  much  space  the  long  hand  has  passed 
over. 

15.  Is  there  a  smaller  portion  of  time  than  a 
minute  measured  by  the  clock  ?  Some  clocks  tick 
60  times  in  a  minute.  Sixty  seconds  make  a  minute. 
30  seconds  are  what  part  of  a  minute  ? 

How  long  does  it  take  the  minute  hand  to  move 
entirely  round  the  face  of  the  clock  ?     Count  the 


MEASURING    TIME.  109 

small  spaces  on  the  face  of  the  clock.  Sixty 
minutes  make  an  hour. 

How  many  minutes  in  2  hours  ?  5  minutes  are 
what  part  of  an  hour  ?  What  time  is  it  by  the 
clock  on  page  108  ? 

If  the  long  hand  were  moved  forward  to  the 
figure  1,  what  time  would  the  clock  show  ?  Where 
will  the  short  hand  of  the  clock  point  when  the 
minute  hand  points  to  6  ?  (Draw  this  upon  your 
slate.     What  time  does  your  clock  show  ?) 

16.  How  many  hours  from  6  in  the  morning 
until  noon  ?  How  many  hours  from  noon  until 
midnight  ?     24  hours  make  a  day. 

How  many  days  make  a  week  ?  How  many 
weeks  make  a  month  ?  Name  the  months  in 
order.  Name  those  which  have  30  days.  How 
many  days  in  February  ? 

60  seconds  (sec.)  =  1  minute  (min.). 

60  minutes  =  1  hour  (h.). 

24  hours  =  1  day  (d.). 

7  days  =  1  week  (w.). 

4  weeks  =  1  month  (ra.). 
12  months ") 

365  days      I  »  *  ***  &** 

17.     MISCELLANEOUS    PROBLEMS. 

1.  If  in  a  half  day  a  man  picks  6  bushels  of 
apples,  and  a  boy  3  bushels;  how  many  bushels 
will  both  pick  in  5  half  days  ? 


HO  ELEMENTARY  ARITHMETIC, 

2.  A  carrier  having  42  New  Year  s  addresses, 
sold  all  but  I  of  them  ;  how  many  did  he  sell  ? 
How  many  had  he  left  ? 

3.  Henry's  age,  which  is  7  years,  is  1  seventh 
of  his  father  s  age  ;    how  old  is  his  father  ? 

4.  What  measure  holds  4  pecks  ?  48  pecks  of 
cranberries  are  how  many  bushels  ? 

5.  A  boy  having  45  cents  spent  |  of  his  money 
for  drawing  paper  and  I  for  pencils ;  how  many 
cents  had  he  left  ? 

6.  How  many  wheels  have  six  freight  cars,  if 
each  car  has  8  wheels  ? 

7.  A  farmer's  boy  fed  to  his  colt  \  a  peck  of 
oats  each  day  for  eight  days ;  how  many  bushels 
is  that  ? 

8.  How  many  pickets  have  7  gates,  if  each  has 
6  pickets  ? 

9.  John  had  5  dimes ;  he  spent  8  cents  for 
stamps,  and  with  the  remainder  took  7  car  rides ; 
what  was  each  fare  ? 

10.  How  many  leaflets  have  7  leaves  of  a  rose- 
bush, if  each  leaf  has  5  ? 

11.  I  bought  a  steak  weighing  a  pound  and  a 
half  ;  how  many  ounces  did  it  weigh  ? 

12.  If  3  pounds  of  coffee  are  used  in  8  days, 
how  many  ounces  are  used  in  1  day  ? 

13.  A  bushel  of  wheat  weighs  60  pounds ;  how 
many  pounds  does  a  peck  weigh  ? 


MISCELLANEOUS  PROBLEMS,  111 

14.  Wheat  bran  weighs  20  pounds  to  the  bushel ; 
what  is  the  weight  of  a  peck  ? 

Does  a  pound  of  wheat  weigh  more  than  a  pound 
of  bran  ?  Weigh  them,  and  notice  the  difference 
in  bulk. 

15.  A  bushel  of  buckwheat  weighs  42  pounds  ; 
what  does  a  peck  weigh  ? 

(is)  Add  \  of  45  to  i  of  49.   (10  45-5-9  +  8  =  ? 
(is)  6x7+8- 25  =  ?     («J  6  x  7  +  (?)  =  50. 
(20)  1  of  45  +  3  =  |  of  what?  (21)  7x7-(?)=42. 

(22)  6  x  8  are  how  many  times  12  ? 

(23)  27-^3x5  +  5-8  =  ? 

18.     ADDING   AND    SUBTRACTING   4's. 
Make  a  table  adding  4  to  numbers  ending  in  4. 
Subtract  4  from  numbers  ending  in  8 ;  4  from 
numbers  ending  in  4. 

4  +  4. 
4      14      24      34      44      54      64      74      84      94 
4444444444 


(1) 

(2) 

(3) 

W 

(5) 

(6) 

212 

444 

929 

424 

394 

793 

444 

943 

393 

492 

834 

339 

422 

222 

994 

333 

919 

449 

244 

779 

933 

629 

343 

333 

444 

322 

243 

333 

424 

934 

422 

988 

928 

837 

233 

382 

244 

232 

933 

292 

392 

893 

444 

424 

397 

486 

398 

329 

243 

787 

683 

766 

629 

892 

937 

347 

677 

226 

552 

458 

112  ELEMENTARY  ARITHMETIC. 

19.    4  +  5,  AND  Keview. 

14      24      34      44      54      64      74     84     94     104 
555555555         5 


(1) 

(2) 

(3) 

w 

(5) 

(6) 

425 

9 

2 

54 

219 

494 

554 

54 

594 

294 

442 

535 

141 

745 

224 

591 

234 

241 

514 

293 

451 

435 

335 

445 

445 

492 

234 

954 

498 

493 

151 

335 

334 

839 

513 

132 

415 

632 

243 

332 

354 

989 

552 

933 

328 

535 

735 

219 

326 

379 

289 

232 

221 

853 

396 

618 

902 

893 

449 

508 

20.      MISCELLANEOUS    PROBLEMS. 

1.  How  many  hours  in  2|  days  ? 

2.  If  a  boy  is  3  minutes  late  at  school,  how 
many  seconds  has  he  lost? 

3.  For  our  school  gardens  we  spent  $1.50  for 
foliage  plants,  $2.10  for  geraniums,  $1  for  tulip 
bulbs,  and  $2  for  roses  and  pansies.  How  much 
money  had  we  left  out  of  $10,  after  paying  for  all  ? 

4.  A  farmer  raises  850  bu.  of  corn,  720  bu.  of 
oats,  560  bu.  of  wheat,  390  bu.  of  barley,  78  bu.  of 
buckwheat ;  how  much  grain  has  he  in  all  ? 

5.  I  had  in  bank  $1125,  and  drew  out  $415  and 
$290  ;  how  much  is  left  in  bank  ? 


MISCELLANEOUS  PROBLEMS.  113 

6.  Johnson  &  Co.,  after  selling  2000  cans  of 
sugar  corn,  had  1500  cans  left ;  how  many  cans 
were  on  sale  at  first  ? 

7.  If  I  have  $230,  how  much  must  I  add  to  it 
to  be  able  to  buy  a  horse  and  buggy  worth  $550  ? 

8.  A  man  receives  $700  for  his  fruit  crop  this 
year,  which  is  $150  more  than  he  received  last 
year ;  how  much  did  he  receive  last  year  ? 

9.  Add  300  to  500,  and  from  this  sum  subtract 
their  difference. 


21.  Subtract  4  from  numbers  ending  in  1,  2, 
and  3.  Give  the  ending  figure  first,  then  the 
whole  remainder. 

11  21      31      41      51      61      71     81      91     101 
444444444         4 

12  22      32      42      52      62      12     82     92     102 
444444444         4 

13  23      33      48      53      63      73     83     93     103 
444444444         4 

21     32     43     52     61     73     80     92     101      100 
44444444         4         4 


Make  tables  subtracting  4  from  numbers  ending 
in  5,  6,  7,  8,  and  9. 

SE 


i                  ELEME 

NTAR1 

r  ARITHMETIC. 

22.  Subtract : 

(1)    (2) 

(3) 

W     (5) 

(6) 

4310    5321 

8234 

6212    8402 

5321 

234    404 

344 

334     314 

334 

7.  9139  -  244  =  ?  13.  9351  -  3544  =  ? 

8.  8123  -  334  =  ?  14.  4352  -  1443  =  ? 

9.  5210-334  =  ?  15.  6231-  344  =  ? 

10.  9431  -  424  =  ?  16.  9132  -  334  =  ? 

11.  5234-325  =  ?  17.  6320-2344  =  ? 

12.  9123-234  =  ?  18.  8123-3254  =  ? 

Make  problems  for  : 

51  -  4  =  47.  83  -  4  =  79.  52  -  4  =  48. 

91  _  4  =  87.  70  -  4  =  66. 

23.   4  +  6,  and  Review. 

4     14     24     34     44     54     64     74     84     94     104 
6666666666        6 


_»_  — 

-    

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

389 

644 

246 

454 

695 

946 

983 

655 

564 

645 

244 

354 

"439 

262 

441 

242 

363 

241 

690 

344 

454 

464 

448 

664 

834 

465 

635 

345 

452 

395 

376 

544 

384 

369 

224 

26 

946 

996 

726 

892 

994 

994 

562 

326 

549 

839 

539 

618 

55 

897 

73 

6S6 

73 

43 

7 

557 

28 

154 

BS 

9 

MISCELLANEOUS  PROBLEMS.  115 

24.     MISCELLANEOUS   PROBLEMS. 

1.  Four  boys  worked  together,  and  received 
$3  for  a  day's  work.  If  they  divide  the  money 
equally,  what  part  will  each  receive  ?  How  many 
cents  will  each  receive  ? 

2.  $9  is  I  of  my  money ;  how  much  money 
have  I? 

3.  5J  qts.  is  I  of  all  the  berries  James  has  to 
sell ;   how  many  quarts  has  he  ? 

4.  George  and  his  two  cousins  received  a  present 
of  2  watermelons ;  they  divided  them  equally ; 
what  was  the  share  of  each  ? 

5.  May,  Ella,  and  Ruth  made  32  pints  of  grape 
jelly,  and  divided  it  equally  ;  what  was  each  one's 
share  of  the  whole  ? 

6.  George  says,  "  61  marbles  is  4  more  than  all 
I  have  ;  "  how  many  marbles  has  he  ? 

Frank  says,  "  Take  4  from  31  and  it  will  leave 
half  of  my  marbles ; "  how  many  marbles  has 
Frank? 

7.  A  boy  standing  30  feet  from  the  edge  of  the 
water,  shot  an  arrow  to  an  island  40  feet  from 
the  shore.  How  far  must  he  go  in  walking  and 
rowing  to  get  the  arrow  and  return  to  the  place  of 
starting  ? 

8.  Bought  10  yd.  of  silk  for  $9.50,  and  10|  yd. 
of  cloth  for  $5.25 ;  how  much  more  did  the  silk 
cost  than  the  cloth  ? 


116  ELEMENTARY  ARITHMETIC. 

9.  A  man  owing  $1000  made  2  payments,  one 
of  $180  and  one  of  $260;  how  much  remained 
unpaid  ? 

10.  A  planing  mill  sells  680  ft.  of  pine  lumber, 
845  ft.  of  poplar,  398  ft.  of  cherry,  480  ft.  of  ash, 
560  ft.  of  walnut,  746  ft.  of  maple.  How  many 
feet  were  sold  ? 


25. 

4  +  7. 

4   14 

24 

34   44 

54   64 

74   84 

94 

7   7 

7 

7   7 

7    7 

7    7 

7 

(1) 

(2) 

(3) 

(±) 

(5) 

(6) 

634 

646 

689 

956 

497 

90 

476 

443 

344 

734 

973 

994 

634 

574 

765 

275 

748 

427 

446 

437 

337 

347 

480 

99 

667 

649 

784 

564 

39 

749 

743 

767 

369 

449 

3 

969 

367 

424 

244 

992 

989 

793 

473 

396 

936 

738 

927 

739 

452 

787 

879 

788 

697 

77 

849 

567 

652 

253 

47 

64 

7.  477  +  743  +  267  +  344  +  598  +  442  +  675 
+  484  +  834  +  646  =  ? 

8.  Add  594,  764,  432,  474,  544,  347,  854,  334, 
788,  and  568. 

9.  Find  the  amount  of  9,  93,  838,  297,  944,  469, 
93,  739,  479,  and  60. 

10.  Find  the  sum  of  9,  34,  897,  378,  949,  983, 
639,  84,  1,  78,  and  78 


MISCELLANEOUS  PROBLEMS.  117 

11.  44  +  987  +  909  +  738  +  493  +  989  +  37 
+  704  +  989  +  44  +  7  =  ? 

12.  839  +  799  +  3  +  488  +  937  +  784  +  478 
+  842  +  649  +  83  +  9  +  9  =  ? 

13.  Add  39,  899,  980,  97,  734,  97,  473,  648, 
783,  68,  4,  7. 

26.    Perform  the  following  examples  : 

1.  8013-    334  =  ?  10.   8354-3545  =  ?      . 

2.  7321-    233  =  ?  11.   7333-2234  =  ? 

3.  8122-    124  =  ?  12.   7421-3432  =  ? 

4.  6124  -    334  =  ?  13.   9341  -    445  =  ? 

5.  9324  -    405  =  ?  14.  2143  -    535  =  ? 

6.  8432  -    445  =  ?  15.   7340  -    534  =  ? 

7.  6242  -  2345  =  ?  16.  7331  -  435  =  ? 
3.  6301-3444  =  ?  17.  6324-1325  =  ? 
9.  6413-1434  =  ?  18.  5412-3444  =  ? 

27.     MISCELLANEOUS   PROBLEMS. 

1.  I  bought  for  Christmas  presents  a  calendar, 
for  which  I  paid  $1,  a  bronze  inkstand  for  $1.50,  a 
paper  weight  for  90  cents,  and  an  album  for  $2.50$ 
what  did  I  pay  for  all  ? 

2.  I  received  $148  for  fruit  trees,  and  $260  for 
shade  trees  ;  the  expense  of  raising  the  fruit  trees 
was  $40,  and  the  shade  trees  $50  ;  what  were  the 
profits  on  each  ? 

3.  Bought  a  house,  lot,  horse,  and  buggy  for 
$1400.  If  I  paid  $600  for  the  lot,  and  $200  for 
the  horse  and  buggy,  *how  much  was  paid  for 
the  house  ? 


118  ELEMENTARY  ARITHMETIC. 

4.  If  I  borrow  at  one  time  $327,  and  at  another 
time  $783,  how  much  do  I  owe  after  paying  $221  ? 

5.  The  greater  of  two  numbers  is  419,  and  the 
less  244  ;  what  is  their  difference  ? 

6.  Henry's  father  was  born  in  1859 ;  how  old 
is  he  now? 

7.  The  sum  of   two  numbers   is  650 ;   one  of 
the  numbers  is  200 ;  what  is  the  other  ? 

28.    review. 

Add  rapidly,  giving  the  ending  figures  first,  then 
the  whole  sum : 

69785979 
22        32        42        52        62         72        82         92 


9 

8 

7 

6 

9 

7 

8 

9 

23 

33 

43 

53 

63 

73 

83 

93 

5 

4 

6 

7 

5 

7 

6 

7 

24 

34 

44 

54 

64 

74 

84 

94 

4 

4 

4 

4 

4 

4 

4 

4 

34 

46 

55 

67 

74 

85 

95 

37 

Add  the  following  lines,  beginning  at  the  left : 

7,  7,  4,  2,  4,  4,  2,  5,  4,  1,  4,  5,  1,  5,  3,  3,  9. 

8,  8,  4,  6,  4,  4,  4,  2,  5,  4,  1,  5,  4,  2,  8,  3,  2,  7. 
5,  4,  4,  9,  8,  4,  5,  1,  4,  4,  2,  9,  3,  7,  2,  3,  6,  4. 

7,  4,  5,  4,  7,  4,  7,  3,  3,  6,  5,  4,  1,  9,  3,  2,  6,  7. 

8,  3,  7,  3,  4,  4,  2,  8,  3,  3,  4,  3,  8,  7,  4,  8,  3,  2. 
,      9,  3,  9,  9,  8,  3,  7,  3,  6,  4,  4,  4,  1,  7,  4,  5,  4,  9. 


REVIEW.  119 

29.  4  +  8. 

4     14     24     34     44     54     64     74     84     94  104 

8888888888  8 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

448 

283 

184 

444 

979 

89 

662 

224 

626 

666 

887 

48 

448 

484 

484 

444 

222 

994 

662 

644 

226 

636 

348 

479 

848 

882 

484 

433 

563 

749 

262 

244 

826 

447 

387 

984 

448 

S66 

284 

384 

744 

936 

880 

288 

841 

327 

399 

994 

526 

447 

28 

773 

393 

649 

38 

267 

939 

668 

968 

99 

7.  Add  384,  384,  348,  314,  958,  328,  733,  493, 
889,  and  269. 

8.  Find  the  sura  of  799,  423,  853, 124,  489,  534, 
928,  298,  988,  and  464. 

9.  84  +  47  +  978  +  288  +  784  +  349  +  899 
+  892  +  699  +  39  +  48  +  84  =  ? 

10.  Find  the  amount  of  83,  387,  938,  974,  949, 
889,  398,  794,  448,  983,  348,  87,  4. 

Subtract : 

1.  8234-1135  =  ?  6.  5234-2245  =  ? 

2.  8012-  245  =  ?  7.  5312-  325  =  ? 

3.  4210-  245  =  ?  8.  9323-5454  =  ? 

4.  6243-2345  =  ?  9.  9000-2001  =  ? 

5.  8544-2035  =  ?  10.  9011-7015  =  ? 


120 


1 

ELEMENTARY  t 

ARITHMETIC. 

30. 

4 

+  9. 

4  14 

24, 

34 

44 

54 

64 

74 

84  94 

104 

9   9 

9 

9 

9 

9 

9 

9 

9   9 

9 

(1) 

(2) 

(3) 

» 

(5) 

(6) 

422 

222 

499 

998 

979 

694 

649 

494 

911 

499 

943 

948 

961 

616 

144 

794 

468 

498 

199 

949 

966 

948 

797 

989 

311 

161 

149 

497 

343 

894 

449 

494 

941 

979 

879 

347 

261 

616 

124 

994 

698 

984 

994 

949 

943 

649 

44 

498 

444 

337 

228 

47 

9 

43 

565  717  828  4  50  38 

7.  Add  98,  949,  899,  981,  444,  96,  974,  443,  78, 
and  68. 

8.  Find  the  amount  of  949,  377,  994,  899,  448, 
79,  794,  948,  98,  and  744. 

9.  Find  the  sum  of  998,  874,  949,  467,  94,  848, 
78,  894,  749,  87,  44,  and  9. 

10.  78  +  90  +  949  +  478  +  44  j-  909  +  887  +  94 
+  989  +  708  +  79  +  3  =  ? 

11.  84  +  939  +  47  +  874  +  478  +  848  +  869 
+  44  +  989  +  787  +  44  +  20  =  ? 

12.  44  +  969  +  448  +  99  +  794  +  447  +  74 
+  878  +  849  +  94  +  49  +  489  =  ? 


MISCELLANEOUS  PROBLEMS.  121 

31.      MISCELLANEOUS    PROBLEMS. 

1.  An  agent  during  the  year  traveled  921  miles 
by  railroad  and  234  miles  by  boat ;  how  much 
more  did  he  travel  by  railroad  than  by  boat  ? 

2.  A  man  had  $5424.  To  his  son  he  gave  $965, 
and  the  remainder  to  his  wife ;  what  was  hk 
wife's  share? 

3.  A  father  and  his  two  sons  earned  $1843  in  a 
year,  the  elder  son  earning  $628,  and  the  younger 
$456  ;  how  much  did  the  father  earn  ? 

4.  What  year  will  it  be,  in  10  years  from  this 
time  ?     In  20  years  ?     In  150  years  ? 

5.  A  merchant  drew  out  of  bank  $650  one  day, 
$327  the  second,  $474  the  third,  and  then  had 
$564  in  bank;  how  much  money  had  he  in  bank 
at  first  ? 

6.  A  man  bought  23  barrels  of  flour  for  $138, 
27  barrels  for  $135,  and  36  barrels  for  $144  ;  how 
many  barrels  did  he  buy,  and  how  many  dollars 
did  he  pay  ? 

32.     review. 
Add: 

9,  9,  4,  9,  9,  4,  7,  8,  4,  8,  3,  7,  3,  8,  6,  4. 

7,  7,  9,  9,  9,  8,  4,  8,  3,  7,  3,  8,  7,  4,  6,  1. 

4,  6,  7,  3,  9,  4,  9,  2,  8,  2,  7,  9,  4,  8,  8,  7. 

4,  9,  9,  3,  4,  4,  6,  4,  8,  3,  7,  3,  8,  4,  9,  2. 

6,  6,  6,  4,  8,  9,  4,  6,  4,  8,  7,  4,  5,  4,  7,  3. 

4,  8,  9,  9,  8,  4,  6,  3,  6,  4,  3,  7,  3,  8,  2,  6. 

6,  7,  6,  2,  4,  8,  3,  9,  4,  4,  9,  4,  8,  9,  3,  5. 


122  ELEMENTARY  ARITHMETIC. 

(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

483  493  497  794  298  646  594  384  799  436 

628  418  782  288  418  443  764  384  423  644 

982  499  698  839  499  574  435  348  853  751 

148  744  242  274  744  437  474  314  124  244 

482  394  879  997  394  649  544  958  489  865 

644  424  449  434  424  767  347  328  534  496 

966  494  894  939  494  424  854  733  928  724 

188  428  324  977  428  396  334  493  298  998 

447  787  998  799  787  787  788  889  988  713 

357  653  338  764  653  567  568  269  464  249 

Subtract : 

1.  8301-2034  =  ?  7.  7322-6543  =  ? 

2.  9312-3543  =  ?  8.  6411-5524  =  ? 

3.  6431-2332  =  ?  9.  3501-3032  =  ? 

4.  8433  -  3544  =  ?  10.  8332  -  6543  =  ? 

5.  9441-5034  =  ?  11.  9420-5033  =  ? 

6.  9400-3623  =  ?  12.  8742-5644  =  ? 

Add: 

(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9) 

989  798  873  889  999  934  498  496  787 

322  979  845  944  844  844  844  844  444 

877  292  149  233  455  955  467  984  485 

713  933  952  724  488  488  327  985  575 

442  244  347  243  319  544  943  438  824 

983  759  732  863  942  223  168  578  493 

524  282  444  143  243  935  484  314  899 

554  444  244  933  354  194  343  993  422 

627  489  536  259  386  938  348  119  644 

978  879  878  778  979  968  798  688  549 


NUMBERS   FROM  FIFTY  TO    SEVENTY.       123 


CHAPTER  V. 

NUMBERS    FROM   FIFTY    TO    SEVENTY. 

1.  How  many  feet  round  a  square        ,  12* feet- 
garden-bed  which   is   12|  feet  on  each     | 
side  ?  S 

Divide  52  apples  into  thirteens. 

52  pecks  are  how  many  bushels?  52  quarts 
are  how  many  pecks  ?  52  quarts  are  how  many 
gallons  ? 

How  many  yards  of  fringe  will  be  used  for  6 
rugs,  if  8§  yards  are  required  for  each  ? 

Some  children  made  a  trimming  of  oak  leaves, 
to  decorate  the  schoolroom  for  autumn :  they 
made  52  feet  in  all.  How  shall  they  divide  it 
to  put  across  the  tops  of  4  blackboards  of  equal 
length  ?     (Drawing.) 

2.  54  cherries  are  how  many  9-cherries  ? 
54-^9  =  ?     6x9  =  ? 

9  is  what  part  of  54  ?  How  many  nines  must 
you  take  from  54  to  leave  9? 

54  equals  how  many  6's?  54  -f-  6  =  ?  9x6  =  ? 
6  is  what  part  of  54  ? 


124  ELEMENTARY  ARITHMETIC. 

Willie  counted  9  joints  in  a  cornstalk;  how- 
many  joints  have  6  such  stalks? 

How  many  sets  of  spoons,  6  in  a  set,  in  54 
spoons  ? 

At  $9  each,  how  many  clocks  can  be  bought  for 
$54? 

From  a  box  of  54  pineapples,  a  dealer  sold  all 
but  !*;  how  many  did  he  sell  ? 

Make  problems  for : 

52  yards  -r  8  =  6£  yards,  each  receives. 
52  cents  ~  8  cents  =      (8-cents  in  52  cents).     54  -i-  9  =  6. 

Give  the  slate  work  in  answer  to  your  problems. 

3.  Draw  55  plums  and  divide  them  into  H's. 
65  -5-11  =  ?    5  x  11  =  ? 

Divide  them  into  5's.  11  five's  are  how  many? 
55  -  5  =  ? 

5  is  what  part  of  55  ?     11  is  what  part  of  55  ? 

4.  Draw  56  flags;  divide  them  into  8's. 
56-8  =  ?     7x8  =  ? 

Divide  the  56  flags  into  7\s.  56  -*-  7  =  ?  8x7  =  ? 
7  is  what  part  of  56  ?    \  of  56  =  ? 

5.      REVIEW. 

11X5=?  56  -=-  7  =  ?  £  of  56  =  ?  7x8=? 
8x7=?  55  -r-  11  =  ?  i  of  57  =  ?  5  X  11$  =  ? 
6  x  9£  =  ?      55+5  =  ?      A  of  55  =  ?       5  X  11J-  =  ? 


NUMBERS  FROM  FIFTY   TO   SEVENTY.        125 

If  I  earn  $8  a  week,  how  much  do  I  earn  in  7 
weeks  ? 

How  many  days  of  school  in  11  school  weeks  of 
5  days  each  ? 

At  $5  each,  how  many  silk  umbrellas  can  be 
bought  for  $55? 

57  quarts  of  ice  cream  were  sold  in  one  day; 
how  many  gallons  were  sold  ? 

I  have  56  flags  to  use  for  decorating  7  win- 
dows ;  how  many  shall  I  use  for  each  window,  if 
they  are  to  be  alike  ? 

Make  problems  for: 
\  of  56  =    8.        i  of57  =  9£.        £  of  57    =    6J. 
6x    9  =  54.       TV  of  55  =  5.  4x13^  =  54. 

Give  slate  work  in  answer  to  problems. 

I  planted  9  grape  cuttings  along  a  walk  57  feet 
in  length ;  how  far  apart  were  they,  if  they  were 
equally  distant  from  each  other?     (Drawing.) 

6.  60  is  how  many  tens  ?  60  -f-  10  =  ?  10  is 
what  part  of  60? 

60  is  how  many  6's  ?  60  -*-  6  =  ?  10  x  6  =  ? 
|  of  60  =  ? 

In  how  many  months  can  I  pay  for  a  sewing 
machine  which  costs  $60,  if  I  pay  $6  a  month  ? 

60  is  how  many  12's  ?  Draw  60  nails  and 
divide  into  12's.  60-12  =  ?  5x12=?  J  of  60  =  ? 
12  is  what  part  of  60  ? 


126  ELEMENTARY  ARITHMETIC. 

A  shoemaker  bought  60  pounds  of  leather,  and 
sold  |  of  it ;  how  many  pounds  did  he  sell  ? 

In  60  hours,  how  many  days  of  12  hours  each  ? 

60  is  how  many  5's  ?  60  ---  5  =  ?  12  X  5  =  ? 
h  of  60  =  ? 

A  man  sold  ^  of  his  load  of  60  watermelons ; 
how  many  did  he  sell  ?     How  many  had  he  left  ? 

60  is  how  many  15's  ?  15  minutes  are  what 
part  of  an  hour? 

How  many  4's  in  60  ?     4  is  what  part  of  60  ? 

A  teacher  divided  60  blocks  of  water  colors 
equally  among  15  pupils ;  how  many  blocks  did 
each  receive  ? 

60  is  how  many  times  30  ?  30  is  what  part  of 
60? 

30  minutes  are  what  part  of  an  hour  ? 


7.      REVIEW. 

6  x  10    =  ? 

4x15=?        60  -f-    6  =  ? 

60  -r-  5  =  ? 

5  x  12    =  ? 

2  x  30    =?       60  +  12  =  ? 

60  -5-  4  =  ? 

If  melons  are  selling  at  3  for  10  cents,  how 
many  can  you  get  for  60  cents  ?     (Drawing.) 

I  paid  5  of  $60  for  my  watch ;  what  did  it  cost  ? 

How  many  hours  in  2\  days  of  24  hours  each  ? 

How  many  days  in  the  months  of  September 
and  November  ? 

A  horse  travels  58  miles  in  8  hours  ;  how  many 
miles  an  hour  is  that  ? 


NUMBERS  FROM  FIFTY  TO  SEVENTY.        127 

2  men  do  a  piece  of  work  in  30  days ;  how  long 
will  it  take  one  man  to  do  the  work  ?  Will  it 
take  1  man  a  longer  or  a  shorter  time  than  2 
men  ? 

Make  problems  for  : 

60  miles  -h  12  miles  =  5  (times). 
60  miles  -f- 12  =  5  miles.     56  hours  -H  7  hours  =  8  (times). 
56  hours  4-7  =  8  hours.       6  X  10  =  60.       5  X  12  =  60. 

8.  Draw  63  nails,  and  divide  them  into  9's. 
63  -  9  =  ?     7x9  =  ?    \  of  63  =  ? 

Mary  planted  63  melon  seeds  in  7  hills.  If  the 
seeds  were  equally  divided,  how  many  were  in  each 
hill? 

Divide  63  into  7's.  63  is  how  many  7's  ? 
9x7  =  ? 

Ella  gathered  some  beechnuts  on  her  way  home 
from  school.  She  says,  u  7  nuts  are  \  of  all  I 
have."     How  many  nuts  has  she  ? 

9.  Draw  64  snow  balls  ;  divide  them  into  8's. 
Eight  boys  are  building  a  snow  fort.     If  each 

makes  8  cannon  balls  of  snow,  how  many  will  they 
have  ?     64  4-  8  =  ?     8x8  =  ?     1  of.  64  =  ? 
Make  problems  for : 

64^8  =  8.      63-v-9  =  7.      624-12  =  5J.     10x6^  =  61. 
\  of  63  =  9.      i  of  64  =  8.      J  of  62  =  10 J. 

10.  66  is  how  many  IVs?  66  ~  11  =  ? 
6xll  =  ?     11  is  what  part  of  66  ? 


128  ELEMENTARY  ARITHMETIC, 

Frank  gave  his  parrot  6  peanuts  in  the  morning 
and  5  at  noon ;  if  the  same  number  are  given  each 
day,  how  many  will  the  parrot  get  in  6  days  ? 

66  is  how  many  6's  ?  $66  will  pay  how  many 
weeks'  board  at  $6  a  week  ?     6  is  what  part  of  66  ? 

11.    70  is  how  many  10's  ?     70  +  10  =  ?     10  is 

what  part  of  70  ?     If  you  have  70  cents  and  spend 
\  of  them,  how  many  cents  have  you  left  ? 

70  is  how  many  7's  ?     7  is  what  part  of  70  ? 

70  days  are  how  many  weeks  ? 

12.      REVIEW. 

1.  18  is  how  many  sevenths  of  63  ? 

2.  If  a  pair  of  curtains  cost  $11,  what  will  6 
pairs  cost? 

3.  How  many  desks  in  a  schoolroom  which  has 
7  rows  and  9  desks  in  each  row  ? 

4.  The  water  in  a  well  is  8J  feet  deep ;  if  this 
is  \  of  the  depth  of  the  well,  how  deep  is  it  ? 

5.  Carl  says,  "  If  my  money  were  divided  into  8 
equal  parts,  one  of  the  parts  would  be  8\  cents.' ' 
How  much  money  has  he  ? 

6.  A  shepherd  carried  7  lambs  across  a  swollen 
stream ;  this  was  \  of  the  whole  flock.  How  many 
sheep  in  the  flock  ? 

Make  problems  for : 

63  trees  -4-  9  trees  =  7  (times). 
63  trees  H-  9     =  7  trees. 


FOURTHS  AND  FIFTHS. 


129 


1 

.3.    Comp 

lete  and  learn 

54- 

~    9  =    6. 

6  x 

9  =  ? 

11 

X2  =  ? 

6x5  =  ? 

54- 

b   6=    9 

9  x 

6  =  P 

12 

X  2  =  ? 

7  x5  =  ? 

55- 

^-11  =    5. 

5x 

11  =  ? 

6 

X  3  =  ? 

8x5  =  ? 

55- 

-    5  =  11. 

11  X 

5  =  ? 

7 

X  3  =  ? 

9x5  =  ? 

56- 

-    8=    7. 

7  X 

8  =  ? 

8 

X  3  =  ? 

10  X  5  =  ? 

56- 

-    7=    8. 

8X 

7  =  ? 

9 

X3  =  ? 

11x5  =  ? 

60- 

-12=    5. 

5x 

12  =  ? 

10 

X3  =  ? 

12  x  5  =  ? 

60- 

-    5  =  12. 

12  x 

5  =  ? 

11 

X  3  =  ? 

6x6  =  ? 

60- 

-10=    6. 

6x 

10  =  ? 

12 

X3  =  ? 

7x6  =  ? 

60- 

-    6  =  10. 

10  X 

6  =  ? 

6 

X  4  =  ? 

8x6  =  ? 

63- 

-    9=    7. 

7X 

9  =  ? 

7 

X  4  =  ? 

9  x  6  =  ? 

63- 

-7=9. 

8  x 

7  =  ? 

8 

X4  =  ? 

10  x  6  =  ? 

64- 

-    8=    8. 

8x 

8  =  ? 

9 

X4  =  ? 

11  X  5  =  ? 

66- 

-    6  =  11. 

6x 

11  =  ? 

10 

X4  =  ? 

7x7  =  ? 

70- 

-10=    7. 

7x 

10  =  ? 

11 

X4  =  ? 

8x7  =  ? 

70- 

-    7  =  10. 

10  X 

7  =  ? 

12 

X4  =  ? 

9x7  =  ? 

FOURTHS   AND   FIFTHS. 


1  or  |  of  a 


Which  is  more,  \  of  a  melon  or  \  ?     4  ui  g 
dollar  ?     1  of  a  dollar  is  how  many  cents  ?     \  of 
a  dollar  is  how  many  cents  ? 

Draw  the  circles  upon  paper  or  upon  slates. 
Into  how  many  equal  parts  is  the  third  circle 
divided  ?  One  of  the  twenty  equal  parts  is  called 
one  twentieth. 


130  ELEMENTARY  ARITHMETIC. 

\  of  the  whole  circle  is  how  many  twentieths  ? 
1  or  |  is  how  many  twentieths  ? 

Find  \  of  the  second  circle.  \  is  how  many 
twentieths  of  the  whole  circle  ? 

Draw  a  regular  pentagon  ;  divide  it  into  5  equal 
triangles.  One  of  the  triangles  is  what  part  of  the 
pentagon  ?  Divide  the  pentagon  into  twentieths. 
One  of  the  triangles  is  how  many  twentieths  of 
the  pentagon  ? 

Look  at  the  circle  and  find  the  answers  to  these 

questions  ? 

J  +  \  =  how  many  twentieths  ? 
£  +  \  =  how  many  twentieths  ? 
£  +  £  =  how  many  twentieths  ? 

f-f-J  =  ?      £  —  J  =  ?      J  of  £  =  what  part  of  the  whole 

circle  ? 
J  +  i=?      £  —  |  xs  ?      J  of  $  =  what  part  of  the  whole  ? 
f  +  J  =  ?      j_i  =  ?      I  of  J  =  what  part  of  the  whole  ? 

John  spent  1  of  his  money  for  a  sled,  and  I  for  a 
pair  of  skates  ;  what  part  of  all  his  money  had 
he  left  ? 

A  grocer  sold  1  of  a  barrel  of  apples  on  Monday, 
and  |  on  Tuesday  ;  what  part  of  the  barrel  re- 
mained unsold  ? 

Look  at  the  circle  and  find  answers  : 

fa  are  how  many  fourths  ?    J-  of  the  circle  is  found  in  fa 

\%  are  how  many  fourths  ?  how  many  times  ? 

\%  are  how  many  fourths  ?    \  is  found  in  \  ? 

\%  are  how  many  fifths  ?      £§  contains  fa  ? 

J-j  are  how  many  tenths  ?     £#  contains  fa  how  many  times  ? 


SQUARE   MEASURE. 


131 


15.     SQUARE   MEASURE. 

One  square  yard. 


Mark  off  in  the  schoolyard  a  flower  bed  which 
shall  measure  a  yard  on  each  side. 

Mark  on  the  schoolroom  floor,  or  on  the  black- 
board, a  square  which  shall  measure  a  yard  on  each 
side.     This  is  called  a  square  yard. 

Divide  the  square  yard  into  9  equal  squares. 
Each  one  of  these  squares  measures  how  much 
on  each  side  ? 

Each  one  of  these  squares  is  called  a  square  foot 

A  square  yard  is  how  many  square  feet  ? 
9  sq.  ft.  =  1  sq.  yd. 


132  ELEMENTARY  ARITHMETIC. 

1  square  foot  is  what  part  of  1  square  yard  ? 

If  you  should  set  out  9  geraniums  in  a  garden 
bed  a  yard  square,  how  much  ground  could  you 
allow  for  each  plant,  allowing  the  same  amount 
for  each  ?     (Drawing.) 

How  many  square  feet  in  2  square  yards  ? 
How  many  square  feet  in  3  square  yards  ? 

Draw  upon  the  board,  or  upon  the  floor  of  the 
school,  3  square  feet ;  inclose  a  space  3  feet  square. 
Which  is  the  larger  space  ?  How  many  times  as 
large  ? 

Draw  and  compare  2  square  feet  with  a  space 
2  feet  square. 

16.  Cut  out  of  paper,  a  square  which  is  1  foot 
on  each  side.  How  many  inches  is  it  on  each 
side? 

Cut  a  square,  which  is  one  inch  on  each  side. 
.  inch  This  is  called  a  square  inch. 

Fold  your  square  foot  of 
paper   into    square    inches. 
First,    into    how    many 
1-inch  strips  shall  you  fold 
.    it? 


1  square  inch. 


_. .  «  .  .  .        One  square  foot  is  how 

This  figure  represents  a  square  inch  *■ 

of  real  size.  many  square  inches? 


1  sq.  ft.  =  144  sq.  in. 


MISCELLANEOUS  PROBLEMS.  133 

Inclose  a  space  upon  your  slate,  or  upon  the 
board,  which  shall  be  1  foot  square.  Divide  this 
square  foot  into  square  inches.  Find  out  how 
many  small  squares  of  patchwork,  each  four 
inches  square,  can  be  cut  from  a  square  foot  of 
calico. 

How  many  can  be  cut  from  a  square  yard  of 
calico  ? 

My  slate  is  9  inches  long  and  7  inches  wide; 
how  many  square  inches  of  surface  has  it  ?  There 
are  7  rows  of  9  square  inches.  7  times  9  square 
inches  =  63  square  inches. 

Find  the  area  (surface)  of  a  flower  bed  which 
is  6  feet  long  and  2  feet  wide. 

The  length  of  a  flower  bed  is  5  feet ;  the  area 
15  square  feet.     What  is  the  width?     (Drawing.) 

17.      MISCELLANEOUS  PROBLEMS. 

1.  How  many  days  in  9  weeks  ? 

2.  How  many  6-inch  pencils  can  you  cut  from 
54  inches  of  lead? 

3.  The  minute  hand  goes  round  the  dial  in  an 
hour;  how  many  minutes  is  it  in  passing  over  ^  of 
this  space  ? 

4.  How  many  square  feet  in  61  square  yards  ? 

5.  A.  confectioner  put  up  52  pounds  of  candy  in 
8  boxes  of  equal  size ;  how  many  pounds  in  each 
box? 


134  ELEMENTARY  ARITHMETIC. 

6.  The  water  in  a  tank  is  51  inches  deep ;  how 
many  feet  deep  is  it  ? 

7.  7|  pecks  of  beans  are  how  many  quarts  ? 

8.  Bessie  had  54  cents ;  she  spent  9  cents  for 
envelopes.  The  remainder  of  her  money  will  pay 
for  how  many  street  car  rides,  if  she  pays  5  cents 
each  time  ? 

9.  A  farmer  having  56  bushels  of  potatoes, 
planted  \  of  them;  how  many  bushels  did  he  plant? 
How  many  pecks?  How  many  bushels  had  he 
left? 

10.  Frank  had  70  cents ;  he  spent  \  of  it  for  a 
ball  of  twine,  f  for  some  nails,  and  with  the  re- 
mainder he  bought  a  reader ;  what  did  his  reader 
cost? 

11.  If  a  cook  uses  6  eggs  each  day,  how  many 
days  will  five  dozen  last  ? 

12.  How  many  sides  have  two  triangles  ?  How 
many  plants  will  be  needed  for  two  triangular 
garden  plats,  if  9  are  planted  on  each  side  ? 
(Draw.) 

13.  If  a  man  works  at  his  trade  nine  hours  a 
day,  how  many  hours  does  he  work  in  a  week  ? 

14.  16  bushels  of  oats  are  how  many  pecks  ? 

15.  I  bought  eight  yards  of  muslin  at  7  cents 
a  yard,  and  gave  in  payment  a  fifty-cent  piece 
and  a  ten-cent  piece ;  what  change  ought  I  to 
receive  ? 


ADDITION  AND   SUBTRACTION  135 

18.      ADDING   AND    SUBTRACTING   5's. 

Add  5  to  numbers  below  100,  which  end  in  5. 
Subtract  5  from  numbers  ending  in  0. 
Make  tables,  subtracting  5  from  numbers  ending 
in  1  and  numbers  ending  in  2. 


19. 

5  +  6. 

5   15 

25 

35   45 

55      65 

75 

85   95 

6   (5 

6 

6    6 

6        6 

6 

6   6 

(1) 

(2) 

(3) 

(4) 

(5) 

(*) 

536 

266 

694 

594 

598 

964 

554 

544 

557 

692 

657 

798 

656 

556 

654 

887 

454 

457 

455 

654 

265 

446 

559 

754 

561 

465 

725 

95 

656 

489 

543 

545 

645 

769 

982 

835 

655 

556 

565 

625 

694 

496 

445 

634 

42 

843 

848 

758 

644 

426 

487 

89 

87 

458 

142 

665 

67 

64 

74 

54 

Add: 

(7)  444,  788,  656,  565,  989,  936,  482,  744,  568,  7,  54. 

(8)  99,  459,  855,  595,  644,  976,  65,  626,  848,  89,  53. 

(9)  75,  896,  559,  60,  696,  982,  444,  688,  655,  57,  859. 

(10)  458,  764,  997,  456,  762,  534,  678,  745,  756,  57,  3. 


20.  5  +  7. 

5 

15 

25 

35   45   55  65 

75 

85 

95 

7 

7 

7 

7    7    7   7 

7 

7 

7 

136 

ELEM1 

ENTARY 

ARITHA 

I ETIC. 

(1) 

(2) 

(3) 

0) 

(5) 

(6) 

567 

312 

553 

469 

495 

354 

537 

735 

525 

795 

898 

557 

753 

375 

735 

986 

975 

585 

355 

535 

355 

748 

756 

526 

757 

557 

755 

275 

389 

959 

373 

753 

335 

475 

75 

147 

535 

377 

555 

855 

726 

743 

555 

533 

651 

581 

847 

494 

583 

876 

958 

68 

87 

299 

254 

516 

778 

8 

57 

359 

21.      MISCELLANEOUS    PROBLEMS. 

1.  Two  numbers,  taken  together,  make  1000. 
One  of  the  numbers  is  320 ;  what  is  the  other 
number  ? 

2.  Find  the  difference  between  534  and  3034. 

3.  Subtract  12  from  1000. 

4.  An  excursion  train  left  Chicago  for  Niagara 
Falls  with  543  passengers.  On  the  way  254  pas- 
sengers left  the  cars  and  162  came  aboard;  how 
many  were  on  the  train  when  it  reached  Niagara 
Falls? 

5.  Morris  paid  50  cents  for  a  hammer,  $1.25 
for  a  saw,  75  cents  for  a  file,  25  cents  for  a  gimlet, 
25  cents  for  a  screw  driver,  $1  for  an  auger,  50 
cents  for  a  chisel,  and  $2  for  a  plane ;  how  much 


MISCELLANEOUS  PROBLEMS.  137 

did  his  tools  cost  him  ?     If  he  should  sell  them  for 
$6,  would  he  gain  or  lose  ? 
Add: 

(6)  789,  572,  757,  484,  979,  834,  548,  674,  668,  898. 

(7)  457,  756,  973,  724,  596,  745,  485,  839,  579,  74. 

(8)  479  +  620  +  7991  +  239  +  497  +  77o  +  48  +  797 
+  872  +  99  +  4  =  ? 

Add: 

(9)  79,  20,  745,  284,  497,  872,  954,  787,  844,  79,  59. 

(10)  975,  726,  548,  875,  775,  239,  443,  878,  797,  775,  90. 

Subtract    5,  giving   the    ending   figure   of   the 
result,  and  then  the  whole  remainder. 

11      22      33      44      55      66      77     88     99     101 
555555555         5 

32      24      53      41      60      82      91     73     54    102 
555555555         5 

61-5  =  ?  94-5  =  ?  63-5  =  ?  92-5  =  ? 
72-5  =  ?  70-5  =  ?  54-5  =  ?  33-5  =  ? 
83-5  =  ?     81-5  =  ?     71-5  =  ?     64-5  =  ? 

Make  tables  subtracting  5  from  numbers  ending 
in  3  and  4. 

22.   5  +  8. 

5  15  25  35  45  55  65  75  85  95 
8888888888 


138  ELEMENTARY  ARITHMETIC, 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

325 

225 

455 

799 

297 

589 

855 

555 

555 

578 

855 

898 

255 

255 

385 

888 

485 

942 

55S 

355 

225 

55 

874 

984 

4:52 

835 

555 

988 

447 

978 

855 

225 

555 

499 

869 

429 

225 

855 

865 

955 

88 

857 

558 

555 

201 

447 

652 

542 

852 

353 

555 

75 

785 

89 

543 

345 

437 

6 

68 

4 

Add: 

(7)  979,  944,  577,  647,  962,  875,  225,  848,  2,  88,  955. 

(8)  945,  973,  878,  223,  755,  274,  855,  955,  84,  89. 

(9)  475,  647,  779,  247,  362,  875,  57,  878,  585,  89,  9. 

(10)  75  +  426  +  858  +  962  +  289  +  528  +  872  +  824 
+  648  +  87  +  54  =  ? 

Find  the  sum  of  : 

(11)  859,  354,  46,  975,  98,  887,  25,  997,  79,  8,  4. 

Add: 

(12)  789,  290,  459,  878,  782,  437,  894,  53,  607,  6,  5. 

23.     Subtract: 

(1)    (2)    (3)    (4)    (5)    (6) 
5514    5065    7617    7748    8119    8094 
1445    5050    3455    3055    5505    4345 


7.  9000  —  1445  =  ?  13.  8122  —  4435=?  19.  7414—4425  =  ? 

8.  8000  —  4405  =  ?  14.  5333  —  1045  =  ?  20.  4444  —  3345  =  ? 

9.  3111  —  2445  =  ?  15.  7303  —  4045  =  ?  21.  9041  —  4445  =  ? 

10.  5111  —  2405  =  ?  16.  4313  —  4144  =  ?  22.  8041  —  1445  =  ? 

11.  7011—4435  =  ?  17.  5113  —  4245  =  ?  23.  5414  —  1415  =  ? 

12.  9112  —  4345  =  ?  18.  9313  —  4344  =  ?  24.  8434  —  1435  =  ? 


MISCELLANEOUS   PROBLEMS.  139 

24.      MISCELLANEOUS   PROBLEMS. 

1.  The  sum  of  3  numbers  is  1345.  Two  of  the 
numbers  are  300  and  400 ;  what  is  the  third  ? 

2.  From  a  cask  containing  900  gallons  of  kero- 
sene I  sold  at  different  times  200  gallons,  165  gal- 
lons, and  150  gallons  ;  how  many  gallons  remained 
in  the  cask  ? 

3.  A  gentleman  bought  a  1000-mile  ticket  on  a 
railroad  for  the  use  of  his  wife,  his  daughter,  his 
son,  and  himself.  His  wife  rode  233  miles,  his 
daughter  289  miles,  his  son  221,  and  he  himself 
rode  the  remainder ;  how  many  miles  did  he  ride  ? 

4.  A  farmer  raised  225  bushels  of  blue  grass 
seed.  He  sowed  74  bushels,  and  sold  95  bushels ; 
how  many  bushels  liad  he  left  ? 

5.  A  has  $639,  B  has  $865,  C  has  $786,  and 
D  has  as  much  as  A,  B,  and  C  ;  how  many  dollars 
hasD? 

6.  A  has  $2400,  B  has  $500  less  than  A,  C  has 
$150  less  than  B ;  how  much  money  has  C? 

25.     review. 
Add: 

(1)  88,  492,  744,  799,  277,  558,  772,  534,  887,  87,  65. 

(2)  599,  540,  489,  77-5,  957,  898,  388,  745,  764,  88,  88. 

(3)  544  +  868  +  454  +  334  +  558  +  663  +  854  +  156 
•f  594  +  288  =  ? 

(4)  989,  587,  659,  884,  497,  958,  52,  598,  844,  68,  65. 


140  ELEMENTARY  ARITHMETIC. 

(5)  878  +  925  +  848  +  89  +  295  +  975  +  424  +  989 
■+  529  +  98  +  973  =  ? 

(6)  799,  947,  864,  577,  959,  795,  495,  844,  577,  58,  4. 

(7)  559,  675,  576,  543,  76,  345,  975,  34,  486,  98,  965  =  ? 

Find  differences: 

1.  9453—  545  =  ?   6.  8441  —  5045  =  ?   11.  7344  —  3545  =  ? 

2.  8453—  544=?   7.  7422  —  5435  =  ?   12.  6412  —  4534  =  ? 

5.  9341—5445=?   8.  4643  —  3004  =  ?   13.  3323  —  2554  =  ? 
4.  8341  —  5345  =  ?   9.  6341—4345  =  ?   14.  9203  —  3405  =  ? 

6.  9623  —  3545  =  ?  10.  7334  —  3025  =  ?   15.  8801—  134  =  ? 


2 

6-  5  +  9, 

5 

15 

25   35 

45  55 

65   75 

85 

95 

9 

9 

9 

9 

9    9 

9   9 

9 

9 

(1) 

(2) 

(3) 

W 

(5) 

797 

958 

87 

768 

355 

950 

885 

590 

55 

478 

.  545 

878 

855 

557 

587 

457 

559 

87 

495 

55 

575 

949 

995 

954 

967 

84 

750 

4 

569 

98 

895 

565 

775 

45 

755 

55 

947 

957 

479 

889 

497 

787 

79 

89 

898 

67 

655 

598 

82 

62 

_____ 

85 

MISCELLANEOUS  PROBLEMS.  141 

27.    Add: 

(6)  895,  258,  978,  45,  554,   645,  546,   795,   606,  8,  4. 

(7)  958,  545,  758,  789,  478,  959,  570,  295,  906,  59,  4. 

(8)  989,  959,  575,  487,  55,  597,  897,  905,  897,  687,  75. 

(9)  895,  587,  798,  855,  566,  855,  975,  989,  589,  95. 

(10)  989,  455,  464,  955,  587,  768,  555,  789,  587,  898,  75. 

(11)  989,  597,  855,  867,  558,  485,  986,  505,  798,  597,  74. 

(12)  (13)  (14)  (15)  (16)  (17) 


325 

515 

585 

995 

959 

899 

598 

959 

515 

587 

575 

575 

512 

151 

954 

798 

689 

856 

955 

555 

151 

455 

552 

789 

195 

599 

959 

787 

784 

585 

915 

911 

191 

378 

499 

897 

255 

155 

515 

595 

585 

594 

457 

535 

995 

556 

348 

854 

575 

287 

277 

688 

787 

89 

977 

242 

347 

565 

465 

65 

28.       MISCELLANEOUS    PROBLEMS, 

1.  In  what  year  was  your  schoolhouso  built? 
How  many  years  have  passed  since  that  time  ? 

How  many  years  have  passed  since  the  discovery 
of  America  by  Columbus  in  1492  ? 

2.  How  many  6-inch  squares  can  be  cut  from 
1  square  foot  of  pasteboard  ?  (Draw  the  square 
foot,  and  divide  into  square  inches.  Draw  the 
6-inch  squares.) 

3.  A  farmer  went  to  town  with  a  load  of  wood, 
which  he  sold  for  $8.     He  bought  25  pounds  of 


142 


ELEMENTARY   ARITHMETIC. 


sugar  for  $2,  8  pounds  of  raisins  for  $1,  2  pounds 
of  tea  for  $1.50,  and  6  pounds  of  coffee  for  $2.10; 
how  much  did  he  spend?  Did  he  sell  his  wood 
for  enough  to  pay  for  his  groceries  ? 

4.  A  grocer  bought  50  barrels  of  apples  and  100 
boxes  of  peaches,  for  which  he  paid  $225.  If  he 
paid  $75  for  the  peaches,  how  much  did  he  pay 
for  the  apples  ? 


Bought  4  lb.  butter, 

@22f 

"      2  lb',  cheese, 

«  18? 

"      3  doz.  eggs, 

"15/ 

"       9  qt.  milk, 

"6/ 

"      2  bu.  potatoes, 

"  65? 

"       2  bu.  carrots, 

« mf 

What  is  the  amount  of 

my  bill  ? 

6.  Bought  9  lb.  rice,        @    7  f  .  . 

"       2   "  tapioca,  "  15  f  ,  . 

"       3   "  sago,       "  \Zf  .  . 

"       5   "   sugar,      "     9f.  . 

"       7   "  prunes,   "     9f.  . 

"       3   "  figs,         "  15 f  .  . 

What  is  the  amount  of  my  bill  ? 


7.  Bought  4  lb.  tea, 
"       ?  "   coffee. 


@  $1.25 
.42 


4  "   raisins,     "        .11  . 
7   "  currants,  "        .09  . 

5  "  crackers,  u       .12  . 
7  "   sugar,       "       .08  . 

What  is  the  whole  amount  ? 


u 
u 
a 
tt 


$ 


BILLS.  143 

8. 


fucaq 


6  ZioAetd  aaiaen    deeat,    @    &  f        ....      jf    .  J^* 

J  >wi//#w  dxdeb,    @   s£<f > 00* 

/  /latnincert A.  <f#* 

7  /own  m&wet &.  )& 

/  ta£ <?#* 

/  dda^e SJS 


°.     $?.    <jMn  /     & 

^  Nashville,  Tenn.,  Feb.  10,  1899. 

Mr.  John  Mitchell, 

Bought  of  J.  D.  Hunt  &  Co., 

2  lb.  coffee,      @  32  f $ 

6  "  crackers,  "  11  f 

3  "   honey,       "18/ 

1  "   Japan  tea .98 

1  doz.  oranges .40 

1  sack  flour 3.89 

Eeceived  payment, 

J.  D.  HUNT  &  CO- 

29.      REVIEW. 

Read  sums  rapidly  : 

32     42     52     62     83     93    63    53    43    33    103 
8697968759        8 


144  ELEMENTARY  ARITHMETIC. 


44 

54 

64 

74 

85 

95 

65 

35 

25 

105 

9 

6 

8 

7 

9 

7 

8 

6 

9 

7 

Add: 

5,  9,  9,  2,  9,  9,  8,  4,  9,  8,  2,  7,  3,  9,  7,  9. 

9,  9,  4,  9,  9,  5,  9,  7,  4,  8,  2,  9,  7,  7,  2,  2. 

7,  5,  8,  9,  5,  8,  9,  4,  9,  7,  4,  6,  4,  7,  0,  8. 

9,  5,  8,  9,  7,  5,  4,  5,  3,  9,  8,  4,  5,  3,  0,  7. 

3,  9,  4,  4,  6,  1,  4,  6,  4,  3,  5,  3,  9,  4,  4,  3,  2,   5,   3. 

4,  7,  6,  2,  3,  8,  9,  1,  5,  4,  1,  7,  4,  8,  2,  6,  4,   3,   5. 
9,  9,  2,  9,  2,  9,  7,  4,  5,  4,  6,  4,  5,  4,  1,  9,  3,  8. 


(1) 

(2) 

(3) 

w 

(5) 

(6) 

(?) 

(8) 

854 

697 

576 

797 

799 

436 

478 

975 

376 

482 

648 

346 

423 

644 

584 

476 

785 

748 

542 

553 

853 

751 

558 

729 

456 

284 

345 

474 

124 

244 

867 

589 

755 

459 

856 

426 

489 

865 

984 

593 

556 

789 

464 

745 

534 

496 

949 

549 

752 

429 

984 

585 

928 

724 

579 

685 

596 

789 

459 

259 

296 

998 

844 

548 

756 

687 

695 

389 

988 

713 

859 

895 

456 

757 

659 

534 

464 

249 

679 

245 

(9)  798  +  557  +  789  +  985  +  557  +  78  +  895  +  559 
+  849  -f  96  +  85  =  ? 

Add: 

(10)  589,  457,  855,  587,  658,  545,  758,  89,  599,  99,  54. 

(11)  58,  79,  594,  957,  85,  474,  545,  874,  689,  77,  8. 

(12)  599,  759,  575,  557,  254,  788,  357,  785,  587,  78,  4. 

(13)  557,  640,  555,  579,  459,  808,  879,  955,  909,  87,  4. 

(14)  45,  575,  678,  554,  508,  370,  757,  545,  959,  86,  54. 

(15)  987,  895,  956,  967,  485,  54,  875,  580,  97,  9,  3. 


FROM  SEVENTY   TO   ONE  HUNDRED.         145 

CHAPTER  VI. 

NUMBERS    FROM    SEVENTY   TO    ONE    HUNDRED. 

1.  Harry  drew  72  lines  upon  his  slate  to  repre- 
sent lamp  posts :  how  many  twelves  did  he  draw  ? 

72  is  how  many  12's  ?  12  is  what  part  of  72  ? 
72  is  how  many  times  \  of  72  ? 

72  —  12=:?    6x12  =  ?    J- of  72  =  ? 

I  paid  $  12,  which  was  \  of  my  money,  for  some 
peach  trees;  how  much  money  had  I  at  first  ? 

Divide  the  72  posts  into  12  equal  groups.  72 
is  how  many  6's  ? 

72  -f-  6  =  ?     12x6  =  ?     ^  of  72  =  ? 

How  many  clocks  can  you  buy  for  $72,  at  $6 
each? 

Make  problems  for : 
6  x  12  =  72.     12  x  6  =  72.     72  -f-  6  =  12.     ^  of  72  =  6 

2.  Draw  72  walnuts :  divide  them  into  8  equal 
groups.  How  many  in  each  group?  72  is  how 
many  9's  ?  Eight  9's  are  how  many  ?  One  of  the 
8  equal  parts  of  72  equals  what  ?  How  many  of 
these  parts  make  the  whole? 

10E 


146  ELEMENTARY  ARITHMETIC. 

72  -r9  =  ?      8x9  =  ?      i  of  72  =  ? 
8  times  )  of  72  =  ?     f  (or  ±)  of  72  =  ?     J  of  72  =  ? 

Put  72  bunches  of  grapes  into  8  baskets ;  what 
part  of  the  whole  will  each  basket  contain,  if  the 
grapes  are  divided  equally  ? 

Divide  the  72  walnuts  into  9  equal  groups : 
how  many  in  each  group  ? 

72  -f-  8  =  ?     9x8  =  ?     J  of  72  =  ? 

8  cents  are  what  part  of  72  cents  ?  72  cents  are 
how  many  times  J  of  72  cents  ? 

Put  72  pounds  of  figs  into  9  boxes  of  equal  size ; 
each  box  will  contain  how  many  pounds  ? 

Divide  72  into  eighteens.  4  eighteens  are  how 
many  ?  How  long  will  a  man  be  in  earning  $72 
who  receives  $18  a  week  ? 


3. 


REVIEW. 


At  9  cents  a  pound,  how  many  pounds  of  prunes 
can  be  bought  for  72  cents  ? 

6  miles  is  ^  of  my  journey ;  what  is  the  whole 
distance  ? 

75  cents  will  buy  how  many  street  car  tickets, 
at  5  cents  each  ? 

I  bought  2  yards  of  flannel  for  75  cents ;  how 
much  was  that  a  yard  ? 


FROM  SEVENTY   TO   ONE  HUNDRED.         147 

If  a  man  earn  $15  a  week,  how  long  will  it  take 
him  to  earn  $75? 

Jennie's  age  is  only  \  the  age  of  her  grandfather, 
who  is  75  years  old  ;  how  old  is  Jennie  ? 
Make  problems  for : 

75  miles  ~  6  miles  =  12£  (times). 
75  miles  -+■  6  =  12^  miles. 

4.  77  is  how  many  elevens  ?  77  4-  11  =  ? 
7  x   11=  ?     j  of  77  =  ? 

A  dealer  in  china  paid  $11  a  set  for  7  sets  of 
dishes;  how  much  did  they  cost  him? 

77  days  are  how  many  weeks  ? 

77  -f-  7  =  ?     11x7  =  ?     ^  of  77  =  ? 

5.  80  is  how  many  tens  ?  80-10  =  ?  8x10  =  ? 
1  of  80  =  ? 

A  farmer  having  80  bushels  of  apples  sold  |, 
used  |,  and  stored  the  remainder;  how  many 
bushels  were  stored  ? 

80  is  how  many  eights  ?  80  ~  8  =  ?  10x8=? 
&  of  80  =  ?     Ten  times  £  of  80  =  ? 

6.  81  nails  are  how  many  9-nails  ?  81  -=-  9  =  ? 
9x9  =  ?     9  times  |  of  81  =  A 

Draw  9  squares,  and  divide  each  one  into  9  equal 
squares  ;  how  many  small  squares  are  there  2 
How  many  square  feet  in  9  square  yards  ? 


148  ELEMENTARY  ARITHMETIC. 

7.  84  equals  how  many  12's  ?  84  eggs  are 
how  many  dozen  ?  84  -*- 12  «  ?  7  X  12  =  ?  12  is 
what  part  of  84  ?     84  inches  are  how  many  feet  ? 

If  $12  is  \  of  the  cost  of  my  bookcase,  what 
was  the  cost  ? 

84  equals  how  many  7's  ?  84  days  are  how 
many  weeks  ?     7  is  what  part  of  84  ? 

I  paid  84  cents  for  a  dozen  papers  of  flower 
seeds ;  how  much  was  that  for  each  paper  ? 

Make  problems  for:     - 

12  x  7  =  84.     84  -T-  7  =  12.     ^  of  84  =  7. 

8.  Draw  88  circles  to  represent  buttons ;  how 
many  ll's  have  you  ?  88  ~  11  =  ?  8  x  11  =  ? 
11  is  what  part  of  88  ? 

If  $11  is  |  the  cost  of  John's  pony,  what  was 
the  cost  ? 

88  is  how  many  8's  ?  8  bushels  are  what  part 
of  88  bushels  ?     88  quarts  are  how  many  pecks? 

88  ~  8  =  ?     11  x  8  =  ?    tV  of  88  =  ? 

If  a  wagon  load  of  potatoes  is  8  bushels,  how 
many  bushels  in  8  wagon  loads? 


U.      F 

REVIEW. 

7  X  12  =  ? 

80- 

-    8  =  ? 

t*t  of  77  =  ? 

12  x  7  =  ? 

11  X    7  =  ? 

77- 

-    7  =  ? 

i  of  81  =  ? 

11  X  8  =  ? 

10  x    8  =  ? 

88- 

-  11  =  ? 

|  of  80  =  ? 

81  ~-  9  =  ? 

9x9  =  ? 

84- 

-    7  =  ? 

A  of  84  =  ? 

tV  of  88  =  n 

FROM  SEVENTY   TO   ONE  HUNDRED.         149 

A  boy  spent  J  of  his  money  for  a  knife,  and  had 
70  cents  left ;  how  much  money  had  he  at  first  ? 

A  gardener  set  out  77  plants,  of  which  |  were 
killed  by  the  frost ;  how  many  were  uninjured  ? 

A  cooking  range  cost  $81,  and  a  small  stove  \  as 
much  ;  what  was  the  cost  of  the  stove  ? 

90  is  how  many  10's  ?     9x10  =  ?     h  of  90  =  ? 

90  is  how  many  9's  ?     9  is  what  part  of  90  ? 

90  cents  are  how  many  dimes  ? 

At  $9  a  dozen,  what  will  10  dozen  hats  cost  ? 

10.  96  is  how  many  12's  ?  96  oysters  are  how 
many  dozen?    8  x  12  =  ?    |of  96  =  ? 

At  12  cents  a  pound,  how  many  pounds  of  maple 
sugar  can  be  bought  for  96  cents?    12  x  | of  96  =  ? 

Divide  96  leaves  into  12  equal  groups ;  how 
many  in  each  group  ?     12  x  8  =  ?     ^  of  96  =  ? 

Plant  96  tomato  plants  in  12  equal  rows;  how 
many  in  each  row  ? 

11.  Mary  drew  some  snow  stars  on  her  slate, 
and  found  that  she  had  9  rows  and  11  in  each  row; 
how   many   had   she  ?      99   is   how   many    ll's  ? 

I  of  99  =  ? 

Ella  worked  11  button  holes  in  one  apron;  how 
many  will  be  required  for  9  aprons,  if  each  requires 
the  same  number  ? 


150  ELEMENTARY  ARITHMETIC. 

Divide  99  into  11  equal  groups;  how  many  in 
each  group  ? 

99  is  how  many  9's  ?     11  nines  are  how  many? 

If  Harry  plants  9  grains  of  corn  in  each  of  11 
hills ;   how  many  grains  does  he  plant  ? 

Make  problems  for : 

ft  of  99  =  9.     11  x  9  =  99.     9x11  =  99. 

12.  Divide  100  silver  dollars  into  tens.  $10 
are  what  part  of  $100  ?  100  cents  are  how  many 
dimes  ? 

George  spent  ^  of  a  dollar  for  a  ball,  ^  for  a 
knife,  and  &  for  a  picture  frame  ;  how  many  cents 
did  he  spend  ?     How  much  money  had  he  left  ? 

50  cents  is  what  part  of  a  dollar  ?  I  of  50  cents 
is  what  part  of  $1  ?  \  of  $1  is  how  many  cents? 
\  of  100  cents  is  how  many  cents  ? 

If  I  pay  $1  for  3  pounds  of  coffee,  how  many 
cents  is  that  a  pound  ? 

At  20  cents  a  pound,  how  many  pounds  of 
butter  can  be  bought  for  $1  ? 

I  bought  6  dozen  eggs  at  the  rate  of  8|  cents 
a  dozen ;  how  much  did  I  pay  for  them  ? 

8  cans  of  corn  at  12|  cents  a  can  cost  how  much  ? 


FROM  SEVENTY  TO   ONE  HUNDRED. 


151 


13.      REVIEW. 


10  X  9  =  ? 
12  x  8  =  ? 

11  X  9  =  ? 


5x20  =  ? 
3  x  33J  =  ? 
,8  X  12    =  ? 


i  of  100  =  ? 
i  of  100  =  ? 
I  of    96  =  ? 


99-t-    9  =  ? 

100  -r- 15  =  t 

96  H-  12  =  ? 


8  dozen  foliage  plants  were  used  in  the  border 
of  a  garden  walk;  how  many  were  used  ? 

At  15  cents  a  yard,  how  many  yards  of  canton 
flannel  can  be  bought  for  $1  ? 

My  fuel  costs  me  $96  a  year;  how  much  is  that 
a  month  ? 

At  121  cents  a  can,  how  many  cans  of  tomatoes 
can  be  bought  for  $1  ? 
Make  problems  for : 

J  of  96  =  12.         J  of  99  =  11.  i  of  100  =  12J. 

8  x  12i  =  100.     12  x  8£  =  100.  96  +  12  =  8. 

96  -7-  8  =  12.       100  -7-  3  =  33J.  100  -h  15  =  6  j. 

14.    Complete  and  learn  : 


72- 

-12=    6. 

6  X  12  =  ? 

84- 

-12=    7. 

7x12  =  ? 

-    6  =  12. 

12  x    6  =  ? 

88- 

-11=    8. 

8  x  11  =  ? 

-    9=    8. 

8  X    9  =  ? 

-    8  =  11. 

11  X    8  =  ? 

-8=9. 

9  x    8  =  ? 

90- 

-10=    9. 

9  X  10  =  ? 

77- 

-11=    7. 

7  X  11  =  ? 

-    9  =  10. 

10  x    9  =  ? 

-    7  =  11. 

11  X    7  =  ? 

96- 

-12=    8. 

8  x  12  =  ? 

80- 

frlO=     8. 

8  X  10  =  ? 

-    8  =  12. 

12  x    8  =  ? 

h    8  =  10. 

10  X    8  =  ? 

99- 

-11=    9. 

9  X  11  =  ? 

81- 

r     9=     9. 

9X    9  =  ? 

-    9  =  11. 

11  X    9  =  ? 

84- 

h    7  =  12. 

12  x    7  =  ? 

100- 

-  10  =  10. 

10  x  10  =  ? 

152  ELEMENTARY  ARITHMETIC. 

15.      REVIEW  OF  TABLES. 

1x2=2  1x3=3  1x4=4 

2x2=4  2x3=6  2x4=8 

3x2=6  3x3=      9  3x4=    12 

4x2=8  4x3=    12  4x4=    16 

5x2  =  10  5x3=    15  5x4=    20 

6x2  =  12  6x3=    18  6x4=    24 

7x2  =  14  7x3=    21  7x4=    28 

8x2  =  16  8x3=    24  8x4=    32 

9x2  =  18  9x3=    27  9x4=    36 

10  X  2  =  20  10  x  3  =  30  10  X  4=  40 

11  X  2  =  22  11  x  3  =  33  11  x  4  =  44 

12  x  2  =  24  12  x  3  =  36  12  x  4  =  48 

1x5=5  1x6=6  1x7=7 

2x5  =  10  2x6=    12  2x7=    14 

3x5  =  15  3x6=    18  3x7=    21 

4x5  =  20  4x6=    24  4x7=    28 

5x5  =  25  5x6=    30  5x7=    35 

6x5  =  30  6x6=    36  6x7=    42 

7x5  =  35  7x6=    42  7x7=    49 

8x5  =  40  8x6=    48  8x7=    56 

9x5  =  45  9x6=    54  9x7=    63 

10  x  5  =  50  10  x  6  =    60  10  x    7  =    70 

11x5  =  55  11x6=    66  11  X    7=    77 

12  x  5  =  60  12  x  6  =    72  12  x    7  =    84 

1x8=8  1x9=      9  IX  10  =10 

2x8  =  16  2x9=    18  2x10=20 

3  x  8  =  24  3  x  9  =    27  3  X  10  =    30 

4x8  =  32  4x9=    36  4x10=40 

5  x  8  =  40  5  x  9  =    45  5  X  10  =    50 

6X8  =  48  6x9=    54  6x10=60 

7x8  =  56  7x9=    63  7x10=70 

8  x  8  =  64  8  x  9  =    72  8  x  10  =    80 

9  x  8  =  72  9  x  9  =  81  9  x  10  =  90 
10  x  8  =  80  10  x  9  =  90  10  x  10  =  100 
11x8  =  88  11X9=  99  11x10  =  110 
12  x  8  =  96  12  x  9  =  108  12  x  10  =  120 


THIRDS,    SIXTHS,   AND  EIGHTHS.  153 

16.     COMPARISON    OP   THIRDS,    SIXTHS.    AND 
EIGHTHS. 


Which  is  more,  §  of  a  dollar  or  I  ?  |  of  a  yard 
or  I  of  a  yard  ?     J  of  a  dollar  or  |  ? 

I  of  a  dollar  is  how  many  cents  ?  |  of  a  dollar 
is  how  many  cents  ? 

Into  how  many  parts  is  the  third  circle  divided 
by  the  lines  ?  Draw  this  circle  upon  your  slate, 
and  divide  each  eighth  into  3  equal  parts. 

Into  how  many  parts  is  the  whole  circle  divided? 
One  of  these  parts  is  called  what  ? 

I  is  equal  to  how  many  twenty-fourths  of  the 
whole  circle  ?     §  are  how  many  twenty-fourths  ? 

Draw  the  second  circle,  which  is  divided  into  6 
equal  parts.  Divide  each  sixth  into  4  equal  parts. 
I  is  how  many  twenty-fourths  of  the  whole  circle? 
§  are  how  many  twenty-fourths  of  the  whole  ? 

|  is  how  many  twenty-fourths  ?  f  are  how  many 
twenty-fourths? 

Look  at  the  first  and  second  circles  shown  on 
this  page.  What  part  of  |  is  1?  What  part  of  \  is 
|?     What  part  of  §  is  \  ? 


154  ELEMENTARY  ARITHMETIC. 

17 •  Draw  a  circle,  and  divide  it  into  24  equal 
parts.  From  your  circle  find  the  answers  to  these 
questions : 

i  -f  £  equals  how  many  twenty-fourths  ? 
i  +  i  equals  how  many  twenty-fourths  ? 

|  of  1  of  the  circle  is  how  many  twenty-fourths 
of  the  whole  ?  J  of  J  is  what  part  of  the  whole  ? 
i  of  I  =  ? 

I  need  I  of  a  yard  of  velvet  for  dress  trimming 
and  I  of  a  yard  for  a  satchel ;  what  part  of  a  yard 
must  I  buy  for  both  ? 

18.     CUBIC    MEASURE. 

How   many  faces   has   a  cube?     What   is   the 
form   of   each  face? 

How  many  edges  has   a 
cube? 

How  many  corners  has  a 
cube? 

Find  a  cube  whose  edges 
are  each  one  inch  long. 
A  cube  whose  edges  are  each  one  inch  long  is 
called  a  cubic  inch. 

Build  a  post  of  1-inch  cubes ;  how  high  a  post 
will  3  such  cubes  make  ?     One  cubic  inch  is  what 


CUBIC  MEASURE.  155 

part  of  the  post  ?  2  cubic  inches  are  what  part  of 
the  post  ? 

How  many  square  inches  in  the  front  face  of  the 
post? 

How  many  cubic  inches  in  2  posts,  if  each  con- 
tains 4  cubic  inches  ? 

19.  1.  Make  a  post  of  one-inch  cubes ;  how 
high  a  post  will  4  such  cubes  make  ?  How  many 
square  inches  in  the  front  face  of  the  post  ?  One 
cubic  inch  is  what  part  of  the  post  ?  2  cubic 
inches  are  what  part  of  the  post  ? 

2.  How  many  one-inch  cubes  in  a  block  3  inches 
long,  3  inches  wide,  and  3  inches  high  ?  (Build 
with  blocks.)  How  many  1-inch  cubes  in  §  of  the 
block?  How  many  square  inches  in  one  of  its 
faces  ? 

3.  How  many  cubic  inches  in 
a  block  of  wood  4  inches  long, 
1  inch  wide,  and  1  inch  thick  ? 

4.  How  many  cubic  inches  in  a  block  4  inches 
long,  2  inches  wide,  and  1  inch 
thick  ?       How    many  rows  of 
4  cubic  inches  each  ?  -■-■-—- 

5.  How  many  cubic  inches  in  a  block  4  inches 
long,   2    inches    wide,    and    2 
inches  thick  ? 


2x4  cubic  inches  =    8  cubic  inches. 

2x8  cubic  inches  =  16  cubic  inches.  4LoI 


156  ELEMENTARY  ARITHMETIC, 

6.  Build  a  solid  4  inches  long,  4  inches  wide, 
and  4  inches  high;  how  many  cubic  inches  will 
it  contain  ?  How  many  square  inches  in  one  of 
its  faces?     Measure  the  distance  round  it. 

7.  How  many  1-inch  cubic  blocks  can  you  pack 
in  a  box  which  is  4  inches  long,  4  inches  wide, 
and   A   inches  high  ? 

8.  U  w  many  1-inch  cubes  of  candy  can  you 
place  in  a  box  6  inches  long,  4  inches  wide,  and 
4  inches  high,  measuring  on  the  inside  of  the 
box? 

9.  Build  a  solid  of  one-inch  cubes  which  shall 
be  12  inches  long,  12  inches  wide,  and  1  inch  high; 
how  many  cubes  did  you  use  ? 

2(X      MISCELLANEOUS  PROBLEMS. 

1.  At  the  rate  of  72  pages  in  9  days,  how  many 
pages  do  I  read  in  a  day? 

2.  Ten  cents,  which  Horace  paid  for  his  draw- 
ing book,  was  one-eighth  of  his  money;  how  much 
had  he  ? 

3.  A  florist  having  7  dozen  roses,  sold  one- 
fourth  of  them ;  how  many  did  he  sell  ? 

4.  If  a  peck  of  berries  cost  96  cents,  what  is 
that  a  quart  ? 

5.  If  you  have  collected  8  dozen  stamps,  of 
which  I  are  6-cent  stamps,  how  many  6-cent 
stamps  have  you? 


MISCELLANEOUS  PROBLEMS.  157 

6.  If  5  cents  is  paid  for  a  cup  of  coffee,  4  cents 
for  fish,  and  2  cents  for  bread,  what  will  6  such 
breakfasts  cost? 

7.  If  I  earn  54  dollars  a  month,  and  save  \  of 
it,  in  how  many  months  will  I  save  72  dollars  ? 

8.  How  many  10-dollar  bills  must  I  pay  for  a 
mirror  that  cost  100  dollars? 

9.  How  many  inches  in  8  feet  ? 

10.  6  dozen  rosebuds  will  be  enough  for  how 
many  bouquets,  if  9  are  used  for  each  one  ? 

11.  If  it  takes  96  tiles  for  a  fireplace,  how 
many  dozen  does  it  take  ? 

12.  I  bought  2  pairs  of  scissors  for  75  cents  ; 
what  was  the  cost  of  1  pair  ? 

13.  A  sheet  of  paper  which  is  8  inches  wide, 
has  a  surface  of  96  square  inches ;  find  the  length. 

14.  What  will  a  roast  of  6  pounds  of  beef  cost, 
at  12|  cents  a  pound  ? 

15.  The  transom  above  the  door  is  3  feet  long 
•  and  2  feet  wide.     How  many  panes  of  glass  will 

it  require,  if  each  pane  is  1  foot  square  ?     (Draw 
picture.) 

16.  How  many  cubic  inches  in  a  block  of 
wood  which  is  7  inches  long,  4  inches  wide,  and 

2  inches  thick  ?     (Drawing.)     If  the  block  were 

3  inches  thick,   how    many    cubic  inches  ?     Four 
inches  thick,  how  many  cubic  inches? 


158  ELEMENTARY  ARITHMETIC. 


^J 

...   REVIEW. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

789 

889 

989 

897 

759 

859 

879 

549 

984 

878 

599 

874 

579 

499 

799 

459 

589 

844 

598 

798 

959 

893 

999 

759 

989 

848 

949 

898 

599 

897 

995 

989 

874 

475 

495 

939 

305 

409 

499 

489 

989 

89 

982 

979 

998 

753 

949 

949 

849 

696 

954 

895 

897 

498 

989 

795 

895 

579 

89 

764 

89 

58 

989 

79 

68 

679 

89 

965 

695 

758 

(8) 

(9) 

(10) 

(U) 

(12) 

(13) 

(14) 

998 

985 

989 

854 

984 

859 

949 

989 

499 

898 

878 

757 

589 

958 

898 

798 

459 

579 

598 

897 

489 

549 

59 

789 

959 

789 

899 

759 

794 

894 

895 

898 

845 

945 

875 

489 

989 

489 

475 

589 

•  489 

949 

737 

548 

958 

749 

989 

989 

589 

899 

978 

879 

878 

594 

984 

898 

657 

589 

898 

987 

898 

609 

859 

98 

876 

756 

876 

89 

89 

795 

(15) 

(16) 

(17) 

(18) 

(19) 

(20) 

(21)  * 

9 

9 

93 

85 

4 

99 

98 

74 

90 

488 

804 

853 

868 

853 

947 

344 

659 

928 

836 

924 

369 

40 

477 

774 

545 

449 

848 

985 

849 

493 

595 

834 

976 

349 

54 

489 

989 

659 

958 

44 

854 

477 

783 

498 

544 

75 

874 

245 

765 

433 

829 

698 

784 

393 

664 

644 

698 

495 

598 

899 

997 

979 

877 

758 

979 

857 

97 

587 

79 

79 

MISCELLANEOUS  PROBLEMS.  159 

Subtract : 

1.  9801—    534=-?  6.  7640  —  2534  =  ?  11.  5101  —  4434  =  ? 

2.  8074  —  2135=?  7.  3141  —  2445  =  ?  12.  8600  —  5534  =  ? 

3.  7004  —  1345=?  8.  3001  —  2154  =  ?  13.  8122  —  6035=? 

4.  9043  —  1534  =  ?  9.  6011—5403  =  ?  14.  5043  —  1415  =  ? 

5.  3842  —  1435  =  ?  10.  3043  —  1415  =  ?  15.  4312—    243  =  ? 

22.      MISCELLANEOUS  PROBLEMS. 

1.  My  slate  lias  a  surface  of  72  square  inches. 
It  is  12  inches  long ;  how  wide  is  it  ? 

2.  If  a  man  earn  $8  a  week,  in  how  many 
weeks  will  he  earn  $96  ? 

3.  I  lost  $50  in  selling  a  piano  for  $280 ;  what 
was  the  value  of  the  piano  ? 

4.  8  men  together  paid  $100  for  some  wheat; 
if  they  received  equal  shares  of  the  wheat,  what 
should  each  man  pay  ? 

5.  A  lady  bought  a  bushel  of  sweet  potatoes  for 
$2.25,  and  gave  in  payment  a  five-dollar  bill;  how 
much  change  should  she  receive  ? 

6.  Bought  20  yards  of  carpet  for  $40,  30  yards 
of  cloth  for  $75,  and  2  pairs  of  curtains  at  $16  a 
pair ;  what  did  I  pay  for  all  ? 

7.  A  real  estate  agent  bought  some  land  for 
$2000 ;  how  much  will  he  gain,  if  he  divides  the 
land  into  4  lots,  and  sells  them  for  $600  each  ? 

8.  If  it  takes  one  man  100  days  to  do  a  piece  of 
work,  in  how  many  days  could  2  men  do  the  same 
work,  working  at  the  same  rate  ?  • 


160  ELEMENTARY  ARITHMETIC. 

9.  If  I  pay  6  cents  for  the  use  of  one  dollar, 
what  should  I  pay  for  the  use  of  5  dollars  at  the 
same  rate  ?  What  must  I  pay  for  the  use  of  12 
dollars  ? 

10.  I  borrowed  $100  for  a  year,  and  paid  6 
cents  on  the  dollar  for  its  use.  How  much  did 
I  pay? 

11.  A  car  line  is  5  miles  long;  if  a  car  makes 
12  round  trips  daily,  how  many  miles  will  it  run 
in  ten  days  ? 

12.  In  a  school  of  45  pupils  I  are  present ;  how 
many  are  absent  ? 

13.  5  gallons  of  cream  were  sold  at  ten  cents  a 
pint ;  how  much  money  did  it  bring  ? 

14.  2  lemons  can  be  bought  for  5  cents  ;  at  that 
rate,  what  is  the  cost  of  2|  dozen  ? 

15.  I  have  a  box  6  inches  long,  4  inches  wide, 
and  2  inches  deep ;  how  many  cubic  inch  blocks 
will  it  hold? 

16.  At  30  cents  a  peck,  what  will  2|  bushels  of 
apples  cost  ? 

17.  My  lot  is  50  feet  wide,  and  four  times  as 
long ;  how  many  yards  of  fence  will  enclose  it  ? 

18.  What  will  2  pounds  4  ounces  of  tea  cost  at 
80  cents  a  pound  ? 


PART    II. 


CHAPTEE    I. 


1.     READING  AND  WRITING   NUMBERS, 

What  is  the  greatest  number  that  can  be  ex- 
pressed by  four  figures? 

If  you  add  one  to  nine  hundred  ninety-nine,  how 
many  ones  have  you  ?  How  many  thousands  ? 
One  thousand  and  nine  thousands  are  how  many 
thousands  ?     How  many  ten-thousands  ? 

Note.  A  box  of  Chinese  toothpicks  can  be  used  in  bundles  of  tens, 
hundreds,  and  thousands,  to  show  the  ten-thousand. 

Write  one  thousand  in  figures.  In  what  place 
does  the  figure  1  stand  ?  If  we  wish  to  express  a 
number  ten  times  as  great  as  1000,  how  shall  we 
represent  it  ?  One  ten-thousand  is  ten  times  as 
great  as  one  thousand.     We  express  the  1  ten- 

11E 


162 


ELEMENTARY  ARITHMETIC. 


thousand  by  writing  the  figure  1  to  the  left  of 
thousands,  in  ten-thousands'  place;  thus,  10,000. 

Write  2  ten-thousands.  2  ten-thousands  are 
how  many  ones  ?  Write  3  ten-thousands  and 
read  the  number  in  two  ways.  (How  many  thou- 
sands ?     How  many  ones  ?) 

2.    Read  the  following  numbers  : 


30,000 

25,400 

15,021 

10,010 

50,000 

36,303 

21,048 

11,001 

90,000 

47,350 

16,743 

15,005 

41,000 

54,707 

28,096 

15,015 

65,000 

90,900 

11,110 

99,999 

How  many  ones  in  each  of  the  last  five  numbers? 
Write  the  following  in  figures  (each  two  as  one 
number) : 


27  thousand  600  ones. 

70  thousand  350  ones. 

6  thousand    70  ones. 

80  thousand      8  ones. 

3.    Write  in  figures : 

Seventeen  thousand  seven. 

Twenty  thousand  two. 

Eighty  thousand  eighty-one. 

Twelve  thousand  twenty- 
one. 

Eleven  thousand  one. 

Eleven  thousand  one  hun- 
dred ten. 


30  thousand  500  ones. 

60  thousand    70  ones. 

95  thousand  200  ones. 

8  thousand      8  ones. 


Seventeen  thousand  seven- 
teen. 

Ninety  thousand  nine. 

Twelve  thousand  twelve. 

Fifty-six  thousand  one  hun- 
dred fifty-six. 

Ten  thousand  ten. 

Eleven  thousand  eleven. 


MULTIPLICATION  AND  DIVISION.  163 

Read  the  following : 

(D  =  500.    M  =  1000.) 
CC.  CCCL.  MDLXXX. 


CCXIX. 

CCCC. 

MDCCCLXXX. 

DCV. 

MDL. 

MDCCXCIX. 

DCXV. 

MDLIX. 

MDCCCLXXXI. 

4.     MULTIPLICATION  AND   DIVISION- 

Taking  one  number  as  many  times  as  there  are 
units  in  another,  is  called  Multiplication. 

Multiplication  is  a  short  method  of  finding  the  sum  of 
two  or  more  equal  numbers. 

Two  times  24  cents  are  how  many  cents  ? 

2  times  $80  =  ?     2  times  396  =  ? 

Two  times  6  ones  are  12  ones.     12  ones  equal  1  ten  and 
2  ones.     Write  the  2  ones  in  ones'  place.     2  times 
9  tens  are  18  tens;  adding  1  ten  we  have  19  tens,         396 
equal  to  1  hundred  and  9  tens.     Write  9  tens  in  2 

tens'   place.      2  times   3  hundreds   are   six  hun-         792 
dreds;  adding  one  hundred  we  have  7  hundreds, 
which  we  write  in  hundreds'  place.     2  times  396  equals  792. 

Find  the  same  result  hy  addition,  and  notice  the  number 
of  ones  added;  the  number  of  tens,  etc. 

396  is  called  the  multiplicand;  it  is  the  number 
to  be  multiplied. 

2  is  called  the  multiplier;  it  is  the  number 
which  shows  how  many  times  the  multiplicand  is 
taken. 

792  is  called  the  product;  it  is  the  result  ob- 
tained by  multiplying. 


164  ELEMENTARY  ARITHMETIC. 

The  multiplicand  and  multiplier  are  called  fac- 
tors of  the  product. 

The  sign  (x)  of  multiplication  is  read  multiplied 
by,  when  the  multiplier  follows  the  multiplicand. 
396  x  2  =  792  is  read,  396  multiplied  by  2  equals 
792. 

When  the  multiplier  precedes  the  multiplicand, 
the  sign  is  read  times.  2  x  396  =  792  is  read 
2  times  396  =  792. 

5.  If  a  man  travel  96  miles  in  a  day,  how  far, 
at  that  rate,  will  he  travel  in  2  days  ? 

96  miles,  traveled  in  1  day. 
2,  number  of  times  96  miles  must  be  taken. 
192  miles,  traveled  in  2  days. 

At  $2  a  box,  what  will  87  boxes  of  lemons  cost? 

$2,  cost  of  1  box. 

87,  number  of  times  $2  must  be  taken. 


$174,  cost  of  87  boxes  of  lemons. 
Make  87  the  multiplier ;  multiply  first  by  7,  then  by  8. 

6.    Multiply  by  2  : 
(1)         (2)         (3)         (4)         (5)         (6)         (7) 
378        856        504        978        709        768        980 
2            2            2            2            2            2            2 

(8)            (9) 
309         2023 
2               2 

(10) 
986 

o 

Ml 

(11)           (12)           (13) 
4507         4659         4709 

2               2               2 

14.  2  multiplied  by  468  =  ?  17.    2  multiplied  by  349  =  ? 

15.  2  "  763  =  ?  18.   2  "  786  =  ? 

16.  2  "  849  =  ?  19.  2  "  605=? 


MULTIPLICATION  AND  DIVISION.  165 

In  the  first  example,  which  number  is  the  multi- 
plicand ?  In  the  last,  which  is  the  multiplicand  ? 
What  are  the  factors  of  the  product  in  the  first 
example  ?  What  are  the  factors  of  the  product  in 
the  tenth  example  ? 

7.  Separating  a  number  into  equal  parts  is 
called  Division. 

How  many  times  can  2  cents  be  taken  out  of  50 
cents  ?  How  many  times  out  of  80  cents  ?  Out 
of  90  cents? 

How  many  2"s  can  be  taken  out  of  9  tens  8  ones  ? 

Show  with  the  counters  that  45  twos  can  be  taken  out  of 
9  tens  or  90  ones,  and  that  4  twos  can  be  taken  out  of  8 
ones.     49  twos  can  be  taken  out  of  9  tens  8  ones. 

Show  that  9  tens  (or  90)  holds  2  ones  4  tens  (or  40) 
times  with  1  ten  remaining.  The  one  ten  is  equal  to  ten 
ones.  Ten  ones  and  8  ones  are  18  ones.  18  ones  holds 
2  ones  9  times. 

How  many  2's  can  be  taken  out  of  972  ? 

2  is  contained  in  9  hundred  4  hundred  times,        2)972 
with  1  hundred  remaining  undivided,  which  is  ~486 

equal  to  10  tens.     10  tens  and  7  tens  are  1 7  tens. 
2  is  contained  in  17  tens  8  tens  times,  with  1  ten  remaining, 
which  is  equal  to  10  ones.     10  ones  and  2  ones  are  12  ones. 
2  is  contained  in  12  ones,  6  times.    2  can  be  taken  out  of  972 
486  times,  or  486  twos  can  be  taken  out  of  972. 

How  many  $2  in  $972  ? 

At  $2  a  barrel,  how  many  barrels  of  potatoes 
can  be  bought  for  $972  ? 


166  ELEMENTARY  ARITHMETIC. 

$2)  $972 

486,  number  of  2-dollars  in  $972. 

486  barrels  of  potatoes,  at  $2  a  barrel,  can  be  bought  for 
$972. 

8.  972  is  called  the  dividend :  it  is  the  number 
to  be  divided. 

2  is  called  the  divisor :  it  shows  the  size  of 
the  equal  numbers  into  which  the  dividend  is  to 
be  separated.  A  divisor  is  called  an  exact  divisor 
when  it  is  contained  in  the  dividend  without  a 
remainder. 

486  is  called  the  quotient :  it  shows  the  num- 
ber of  equal  numbers  into  which  the  dividend  has 
been  separated.         , 

The  divisor  and  quotient  are  factors  (makers)  of 
the  dividend. 

The  product  of  the  divisor  and  the  quotient, 
plus  the  remainder,  is  equal  to  the  dividend. 

Division  may  be  expressed  or  indicated  by  the 
sign  (V) ,  or  by  writing  the  dividend  over  the  divi- 
sor with  a  line  between  them.  Each  of  the  ex- 
pressions, 24  -f-  2  =  12  and  f  =  12,  may  be  read, 
24  divided  hy  2  equals  12. 

Divide  by  2 : 


1.  7398 

4. 

8604 

7. 

7176 

10. 

2015 

2.  8249 

5. 

7170 

8. 

1257 

11. 

4819 

3,  9781 

6. 

9410 

9. 

6729 

12. 

9197 

MULTIPLICATION  AND  DIVISION.  167 

9.  One  half  of  90  cents  is  how  many  cents  ? 
Divide  9  dimes  equally  between  2  boys;    how 

many  dimes  will  each  receive  ? 

Find  1  of  9  tens  8  ones. 

J  of  9  tens  is  4  tens,  with  1  ten  remaining,  which  is  equal 
to  ten  ones.  Ten  ones  and  8  ones  are  18  ones.  J  of  18 
ones  is  9  ones.  One-half  of  9  tens  8  ones  is  49  ones.  Show 
by  counters. 

A  man  divided  $972  equally  between  his  two 
children  ;  how  much  money  did  each  receive  ? 
2)  $972  money  to  be  divided. 
$486  each  child  received. 

10.  Separate  400  into  two  equal  parts;  into 
five  equal  parts.  Separating  a  number  into  a  given 
number  of  equal  parts  is  called  Partition. 

Find  $  of : 

1.  9875      3.  9347      5.  3098      7.  $8101        9.  7003  bushels. 

2.  6001      4.  7190      6.  5729      8.  $7900      10.  5045  pecks. 

11.  1.  If  a  man  travel  286  miles  in  2  days,  at 
that  rate  how  far  will  he  travel  in  one  day  ? 

2.  A  clock  strikes  312  times  in  2  days;  how 
many  times  does  it  strike  in  1  day  ? 

3.  How  many  times  must  we  take  the  number 
2  to  make  652  ? 

4.  If  a  man  earn  $2  a  day,  how  long  will  it 
take  him  to  earn  $550?  s 

5.  A  bookseller  paid  $114  for  photograph 
albums  at  $2  each ;  how  many  did  he  buy  ? 


168  ELEMENTARY  ARITHMETIC. 

6.  A  gardener  sold  750  strawberry  plants,  which 
was  |  of  all  he  had ;  how  many  had  he  ? 

7.  What  number  multiplied  by  2  will  produce 
1680  ? 

12.     MULTIPLYING   AND    DIVIDING   BY  3. 

Find  the  products  of  : 

1.  3086x3       4.   3006x3       7.  3009x3       10.   4123x3 

2.  3097x3       5.   3246x3       8.   2549x3       11.   2867x3 

3.  2786x3       6.   3269x3       9.    3369x3       12.   3009x3 

13.   3  multiplied  by  2738  =  ?      14.   3  multiplied  by  3108  =  ? 
Find  the  quotients  of : 

1.  3687  -  3       3.   7891  h- 3       5.   2501  -r-  3       7.   9108 -f- 3 

2.  3456  -r-  3       4.   5476-3        6.    7057-4-3        8.   8310-3 

13.    1.    How  many  3-cents  in  3564  cents? 

2.  How  many  yards  in  a  coil  of  wire  which 
contains  2500  feet? 

3.  What  will  687  yards  of  cloth  cost,  at  $3  a 
yard  ? 

4.  A  man  earned  $12  a  week  and  saved  $3; 
in  how  many  weeks,  at  that  rate,  will  he  save 
$450? 

5.  If  a  steamer  can  run  278  miles  a  day,  how 
far  can  it  run  in  3  days  ? 

6.  $241  is  I  of  my  money ;  how  much  money 
have  I ? 


REVIEW.  169 

7.  Three  times  I  of  $300  is  the  price  of  a  lot; 
what  is  the  value  of  the  lot  ? 

8.  Find  dividends: 

3)_     3) 3)_     3)_ 

241       335       35J       680 

How  is  the  dividend  found,  when  divisor  and 
quotient  are  given  ?  What  are  the  factors  of  the 
dividend  ? 

14.    review. 


(1) 

(2) 

(3) 

W 

(5) 

(6) 

(?) 

(8) 

9 

544 

45 

96 

7 

95 

84 

497 

753 

688 

906 

995 

673 

994 

874 

356 

446 

995 

399 

437 

255 

77 

459 

643 

894 

466 

465 

354 

577 

952 

698 

355 

526 

748 

736 

467 

688 

594 

765 

556 

665 

459 

847 

284 

875 

549 

455 

533 

949 

332 

984 

437 

146 

458 

793 

486 

536 

795 

144 

345 

595 

477 

745 

959 

246 

87 

738 

408 

379 

727 

56 

36 

989 

9 

77 

98 

897 

78 

868 

887 

(9)  (10)  (11)  (12)  (13)  (14)  (15)  (16) 
444  94  79  9  988  44  98  9 
347    93   794   449   532   836   985    97 


652 

944 

346 

944 

898 

589 

637 

954 

977 

427 

443 

895 

452 

555 

254 

446 

844 

959 

565 

844 

365 

478 

536 

778 

476 

494 

499 

499 

858 

687 

688 

924 

994 

439 

432 

949 

447 

535 

544 

559 

444 

487 

564 

477 

855 

754 

395 

485 

168 

496 

49£ 

246 

879 

937 

797 

898 

987 

787 

979 

998 

959 

687 

79 

959 

170  ELEMENTARY  ARITHMETIC. 

15.    Subtract  : 

1.  14554  —  6555=?      6.   15643  —  5504  =  ?  11.   15043  —  5505  =  ? 

2.  10753  —  2755  =  ?       7.  10042  —  5143  =  ?  12.   12544  —  5505  =  ? 

3.  12502  —  3745  =  ?      8.  12455  —  6235  =  ?  13.   10451  —  7043  =  ? 

4.  13404  —  5545  =  ?      9.   15543  —  7005  =  ?  14.  14872  —  6235=? 

5.  13450  —  5054  =  ?    10.  14046  —  1504=?  15.  10001  —  9876=? 


16.      ORAL  REVIEW. 

1.  I  have  4  pictures  to  be  hung,  each  needing 
7  feet  of  wire ;  how  much  will  it  cost  at  3  cents  a 
yard  ? 

2.  From  a  piece  of  cloth  containing  25  yards, 
a  tailor  cut  8  suits  of  clothes,  each  containing  2f 
yards ;  how  many  yards  remained  ? 

3.  Henry  gathered  i  of  a  bushel  of  walnuts  and 
2\  bushels  of  hickory  nuts ;  how  many  pecks  did  he 
gather  ? 

4.  If  4  yards  of  muslin  cost  6  dimes,  how  many 
yards  can  I  get  for  $1  ? 

5.  I  bought  a  remnant  of  ribbon  12  inches  long, 
which  was  worth  9  cents  per  yard ;  what  change 
should  the  clerk  give  me  for  a  dime  ? 

6.  If  a  piece  of  ribbon  \  of  a  yard  long  costs 
5  cents,  how  many  yards  could  I  have  bought  for 
50  cents  ? 

7.  Walter  bought  a  book  for  50  cents ;  this  is 
i  of  the  cost  of  his  skates,  and  \  the  cost  of  his 
sled ;  how  much  will  his  skates  and  sled  cost  ? 


MULTIPLICATION  AND  DIVISION,  171 

8.  If  you  get  6  pounds  of  sugar  for  50  cents, 
how  much  would  18  pounds  cost  you  ? 

9.  Asphalt  pavement  is  being  laid  from  Sev- 
enth to  Twelfth  Street,  at  the  rate  of  one  third  of 
a  block  per  day ;  how  long  will  it  take  ? 

10.  If  15  apples  are  sold  for  5  cents,  what  is 
the  price  per  dozen? 

11.  |  of  60  yards  is  how  many  feet  ? 

12.  How  many  3-ounce  packages  of  nutmegs 
can  be  put  up  from  2\  pounds  ? 


17. 

1  +  1  =  ? 

i-i  =  ? 

i-t  =  ? 

4x  i  =  ? 

£  +  !  =  ? 

|-i  =  ? 

§-*  =  ? 

3xi  =  ? 

i-t  =  ? 

4-1  =  ? 

£-!  =  ? 

iofi  =  ? 

4x|  =  ? 

iofi  =  ? 

2  x  |  =  ? 

5xf  =  ? 

3  x  i  =  ? 

2X1  =  ? 

3x  t  =  ? 

6xj  =  ? 

*ofi  =  ? 

5X1  =  ? 

2  x  |  =  ? 

7  X  |  =  ? 

*ofi  =  ? 

3x  §  =  ? 

2XJ  =  ? 

8x  i  =  ? 

18.     MULTIPLYING  AND  DIVIDING   BY  4  AND  5. 

Find  products  of : 

1.  $56x4:         3.  968x4  5.   2079X4  7.   1976x4 

2.  978  x  4         4.   989  x  4  6.   2098  x  4  8.   1678  x  4 

Find  quotients  of : 

1.  6789^-4  3.  14009 -f- 4  5.  31033  +  4  7.  34035-^4 

2.  2135^4  4.  15203 -T- 4  6.  67890-4  8.  39393 -f- 4 


172  ELEMENTARY  ARITHMETIC. 

1.  If  4  men  can  lay  6400  bricks  in  a  day,  how 
many  will  one  man  lay  in  the  same  time,  working 
at  the  same  rate  ? 

2.  1260  bushels  of  apples  are  how  many  pecks? 

3.  How  many  square  inches  in  4  square  feet  ? 

19.   Find  products  of : 

1.  1856x5       3.   2765x5       5.  3579x5       7.  1948x5 

2.  2708x5        4.   3769x5       6.   1978x5       8.  1067x5 

Divide  by  5 : 

1.  19290        4.   18605        7.   46979         10.   47464 

2.  94806        5.  43441        8.   37300        11.    89180 

3.  31433        6.  38024        9.   54306        12.   34744 

1.  How  many  5-cents  in  5895  cents? 

2.  What  is  the  weight  of  a  bushel  of  wheat,  if 
5  bushels  weigh  300  pounds  ? 

3.  A  man  divided  $9850  equally  among  three 
sons  and  two  daughters ;  how  much  did  each 
receive  ? 

4.  Which  is  greater,  \  of  3  times  30,  or  \  of  4 
times  20  ?     How  much  greater  ? 

5.  A  man  bought  a  coat  for  $24,  a  hat  for  $5, 
a  pair  of  shoes  for  $6,  and  a  cravat  for  $1.50; 
how  much  did  they  all  cost  ?  In  paying  the  bill 
he  gave  the  merchant  five-dollar  bills.  How 
many  bills  did  he  use,  and  what  change  should 
he  receive  ? 


UNITED   STATES  MONEY.  173 

CHAPTEE  II. 
1.     UNITED   STATES  MONEY. 

Read  the  following : 

$426.37  $4003.90  $50035.05 

$200.02  $9040.09  $16200.15 

$187.07  $1919.19  $70017.17 

Express  in  figures : 

1.  Nine  hundred  sixty-seven  dollars  eight  cents. 

2.  Fifty-two  thousand  dollars  twelve  cents. 

3.  Forty-one  thousand  eleven  dollars  seven  cents. 

4.  Eleven  thousand  one  hundred  dollars  one  cent. 

What  will  4  barrels  of  flour  cost,  at    $6.80  a 

barrel ? 

$6.80  cost  of  one  barrel. 
4 


$27.20  cost  of  4  barrels. 
Multiply  as  in  simple  numbers,  and  if  there  are  cents 
in  the  multiplicand,  point  off  two  places  for  cents  in  the 
product. 


Ri 

id  products : 

l. 

$16.15  x  3 

4. 

$286.04  X  3 

7. 

$0.89  X  4 

2. 

$26.10  x  2 

5. 

$480.70  x  4 

8. 

$0.75  x  3 

3. 

$45.01  x  5 

6. 

$0.85  X  5 

9. 

$0.90  x  5 

174  ELEMENTARY  ARITHMETIC. 

2.  What  is  the  cost  of  a  bushel  of  apples,  if  5 
bushels  are  sold  for  $6  ? 

5  )  $6.00  cost  of  five  bushels. 
$1.20  cost  of  one  bushel. 
If  the  dividend  contains  no  cents,  annex  two  ciphers, 
separated  from  dollars  by  a  period.     Divide  as  in  simple 
numbers,  and  separate  dollars  from  cents  in  the  quotient. 

When  sugar  is  selling  at  5  cents  a  pound,  how 

many  pounds  can  be  bought  for  $6  ? 

.05 )  $6.00  money  to  be  expended. 

120  number  of  5-cents  in  600  cents,  or  $6. 
120  pounds  of  sugar  at  5  cents  a  pound  can  be  bought 
for  $6. 

Find  quotients : 

1.  $416.57 -r- 5         4.   $10050.50-^3        7.   $11213.05-^2 

2.  $312.22 -T- 4         5.    $40380.90^2        8.   $16008.00^5 

3.  $700,07  4-3         6.   $25600.00  h- 4        9.   $90500.00-^4 

3.     FACTORS. 

An  integer  is  a  whole  number  (so  called  to  dis- 
tinguish it  from  a  fraction). 

1.  What  two  integers  multiplied  together  will 
produce  8  ?  14  ?  16  ?  21  ?  30? 

A  factor  of  a  number  is  any  one  of  two  or  more 
integers  which  multiplied  together  produce  the 
number. 

2.  Give  all  the  pairs  of  factors  of  32,  36,  28, 

45,  48,  and  50. 

32=j4x8 
(2x  16 


MULTIPLICATION  AND  DIVISION.  175 

3.  What  three  numbers  multiplied  together  will 
produce  16?     (2x2x4  =  16.) 

4.  What  three  numbers  multiplied  together  will 
produce  18?  24  ?  27  ?  28  ?  30  ?  32  ?  40?  45  ? 

A  number  which  is  the  product  of  other  factors 
besides  itself  and  one  is  called  a  composite  number. 

Note.  A  composite  number  is  so  called  because  composed  of,  or 
produced  by,  factors. 

5.  Write  the  composite  numbers  between  20 
and  40.     Between  60  and  90. 

4*  An  even  number  is  one  which  can  be  divided 
by  2  without  a  remainder. 

An  odd  number  is  one  which  cannot  be  divided 
by  2  without  a  remainder. 

Write  the  odd  numbers  between  30  and  40. 
Which  of  these  odd  numbers  are  composite? 

5.     MULTIPLYING   AND   DIVIDING   BY   6. 

Multiply  the  following  numbers  by  6 : 

1.  9874   4.  5907    7.  7308    10.  10396 

2.  3009    5.  8679    8.  5897    11.  12958 

3.  10068    6.  11948    9.  16087    12.  11769 

Divide  the  following  by  6 : 

1.  32430    4.  44445    7.  56457  10.  17171 

2.  34850    5.  46847    8.  58259  11.  19191 

3.  37838    6.  49250    9.  57456  12.  31433 


176  ELEMENTARY  ARITHMETIC. 

6.  1.  What  is  received  for  a  bushel  of  black- 
berries which  is  sold  at  the  rate  of  6  cents  a 
quart  ? 

2.  A  grocer  paid  $23.16  for  honey  at  6  cents  a 
pound ;  how  many  pounds  did  he  buy  ? 

3.  163|  miles  is  one  sixth  of  the  distance  from 
New  York  to  Chicago ;  what  is  the  distance  ? 

4.  Bought  6  cords  of  wood  at  $4.90  a  cord,  and 
gave  in  payment  5  barrels  of  flour ;  how  much 
was  the  flour  per  barrel  ? 

5.  How  many  days  in  6  years  ? 

7.     ADDITION  AND   SUBTRACTION. 
6  +  6    AND    REVIEW. 


6 

16  26 

36  46 

56      66 

76 

86     96 

6 

JL  A 

6   6 

6   6 

6 

A       6 

(1) 

(2) 

(3) 

(*) 

(5) 

(6) 

96 

965 

955 

7659 

6989 

4665 

594 

224 

436 

4444 

5659 

7654 

662 

655 

596 

7363 

8346 

4469 

259 

386 

695 

6735 

3653 

7653 

569 

596 

39 

6646 

673 

4986 

756 

765 

566 

8686 

968 

7866 

684 

939 

64 

7895 

6366 

6459 

566 

646 

995 

5563 

9681 

2794 

437 

358 

668 

8349 

7988 

9778 

79 

788 

999 

6879 

7687 

6899 

ADDITION  AND   SUBTRACTION.  177 

8.    Subtraction  ot   6   from  numbers  ending  in 
any  one  of  the  digits. 


16 

27 

38 

49 

50 

61 

72 

83 

94 

95   10< 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6    ( 

Make  tables  subtracting  6  from  numbers  ending 
in  0,  1,  2,  3,  4,  and  5. 
Subtract : 

1.  26345  —  2556=?   7.  59213  —  2505  =  ?  13.  23543  —  1554  =  ? 

2.  15043  —  1546  =  ?   8.  68334  —  1056=?  14.  50354  —  5646=? 
8.  19411  —  1506=?   9.  70035  —  6056  =  ?  15.  47352  —  4353  =  ? 

4.  27522  —  3615=?  10.  20053  —  2455=?  16.  30334  —  3455  =  ? 

5.  35432  —  4546  =  ?  11.  49543  —  4546=?  17.  23451—   56  =  ? 
6.43543  —  1456=?  12.30533—   36=?  18.10052  —  1554=? 

9.  1.  I  give  a  fifty-dollar  bill  in  paying  an 
account  of  $36.37;  how  much  change  should  I 
get? 

2.  The  difference  between  two  numbers  is  1160. 
The  smaller  number  is  8340 ;  what  is  the  larger 
number  ? 

3.  Washington  was  born  in  1732;  in  what  year 
was  he  57  years  old  ? 

4.  260  bushels  of  potatoes  is  55  bushels  more 
than  a  grocer  sold  during  the  month  of  Septem- 
ber; how  many  bushels  did  he  sell? 

5.  Bought  30  yards  of  cloth  for  $96.90,  20 
yards  of  carpet  for  $40,  and  two  pairs  of  curtains 
for  $16.50;  what  did  all  cost? 

12E 


178  ELEMENTARY  ARITHMETIC. 

6.  How  many  strips  of  paper  bordering,  each 
5  yards  in  length,  will  be  required  for  a  room 
which  is  30  feet  square  ?     (Make  a  drawing.) 

7.  Bought  a  farm  for  $13716,  and  sold  it  for 
$13379;  did  I  gain  or  lose? 

8.  A  saleswoman  earns  $0.89  a  day,  and  her 
expenses  are  $3.75  a  week;  how  much  does  sh£ 
save  in  6  weeks  ? 

9.  I  bought  a  house  for  $6500,  spent  $1876  in 
improvements,  and  then  sold  it  for  $9155 ;  how 
much  did  I  gain? 

10.  Of  a  railroad  2465  miles  long,  1266  miles 
are  double  track ;  how  many  miles  are  single 
track  ? 

10.      ORAL  REVIEW. 

1.  If  4  pounds  of  chocolate  cost  58  cents,  how 
many  cents  is  that  a  pound  ? 

2.  If  a  man  travel  15  miles  in  3  hours,  how  far 
at  this  rate  will  he  travel  in  9  hours  ? 

3.  What  will  |  of  a  pound  of  candy  cost,  at  3 
cents  an  ounce  ? 

4.  Bought  |  bushel  of  apples  and  \  bushel  of 
peaches ;  what  part  of  a  bushel  have  I  ?  How 
many  quarts  did  I  buy? 

5.  |  of  24  +  1  of  16  are  how  many  times  7  ? 

6.  A  man  had  24  horses;  after  selling  f  of 
them,  he  lost  1  of  them;  how  many  were  left? 


ORAL   REVIEW.  179 

7.  Bought  4§  pounds  of  grapes  at  6  cents  a 
pound ;  how  much  did  they  cost  ? 

8.  If  3  pounds  of  almonds  cost  25  cents,  what 
will  5  pounds  cost  at  the  same  rate? 

9.  A  boy  gave  to  his  sister  \  of  an  orange,  to 
his  brother  \  as  much  as  he  gave  to  his  sister,  and 
kept  the  rest  himself ;  what  part  did  he  keep  ? 

10.  If  two  pounds  of  cheese  cost  36  cents,  what 
will  half  a  pound  cost  ? 

11.  The  ages  of  4  boys  are  7,  9,  8,  and  12 ; 
what  is  the  average  of  their  ages  ? 

12.  A  bushel  of  corn  weighs  56  pounds;  what 
is  the  weight  of  a  peck  ?  a  half  peck  ?  a  quart  ? 

13.  A  boy  living  \  mile  from  school,  who  goes 
home  to  dinner,  will  walk  how  many  miles  each 
week  in  going  to  and  from,  school  ? 

14.  Buy  4  dozen  pencils  at  30  cents  a  dozen, 
and  sell  them  at  4  cents  apiece ;  what  is  gained  ? 

15.  With  what  you  have  gained  buy  3  dozen 
erasers  and  sell  them  at  6  cents  apiece ;  how  much 
do  you  gain  this  time,  and  how  much  money  have 
you  altogether  ? 

11.    Solve  : 

*  +  }  =  ?  |'-|  =  f  |  -  i  =  ?         3xi  =  ? 

i  +  £  =  ?         f-i  =  ?         f-f==?         6xj  =  ? 


180  ELEMENTARY  ARITHMETIC. 

J  +  J  =  how  many  twelfths  ?     ft  are  how  many  fourths  ? 
£  +  J  =  how  many  twelfths  ?     \%  are  how  many  sixths  ? 
■j^  =  how  many  sixths  ?        J  of  -^  is  what  part  of  a  whole  ? 
^  =  how  many  fourths  ?      J  of  J  is  what  part  of  a  whole  ? 
ft  =  how  many  halves  ?       J  of  J  is  what  part  of  a  whole  ? 
Which  is  more,  ft  of  a  dollar  or  }  of  a  dollar? 

12.      6+7   AND   REVIEW. 


6   16 

26 

36   46 

56   66 

76 

86   96 

7   7 

7 

7   7 

7    7 

7 

7    7 

(1) 

(2) 

(3) 

w 

(5)  . 

(6) 

996 

967 

768 

997 

896 

6886 

767 

953 

437 

746 

9565 

4553 

577 

667 

762 

654 

433 

5665 

877 

336 

255 

979 

7766 

636 

676 

57 

646 

469 

6568 

8387 

554 

656 

656 

463 

9895 

656 

983 

364 

765 

539 

4647 

9439 

767 

65 

276 

697 

676 

7475 

127 

889 

797 

678 

7568 

8518 

899 

79 

959 

988 

989 

798 

Add: 

(7)  979,   969,   787,   696,   969,   878,   997,   788,  979,  89. 

(8)  76,   967,   899,   798,   697,   876,   968,  79,  577,  87,  9. 

(9)  78,   969,   697,   786,   978,   869,   979,   779,   6,   89. 
(10)   707,   966,   979,   799,   689,   76,   867,   978,   706,   66. 

13.  1.  From  the  sum  of  3250  and  6845  take 
their  difference. 

2.  A  mechanic  earns  $3.75  a  day,  and  spends 
$2.50  a  day ;  how  much  does  he  save  in  a  week? 


REVIEW.  181 

3.  A  man  had  $526  in  bank;  he  drew  out 
$149,  deposited  $358,  and  then  drew  out  $76; 
how  much  remained  to  his  credit  in  the  bank  ? 

4.  On  the  first  day  of  January  a  man  rented  a 
house  at  $480  a  year,  and  occupied  it  until  July 
1st ;  how  much  rent  should  he  pay  ? 

5.  Bought  760  barrels  of  flour,  at  $6  a  barrel, 
and  sold  it  for  $5342  ;  how  much  was  gained  ? 


14. 

6  + 

8  AND  REVIEW. 

Read  endings : 

26 

46   36 

96 

56       76 

66       86 

106 

8 

8    8 

8 

8    8 

8    8 

8 

(1) 

(2) 

(3) 

(4) 

(«> 

(6) 

969 

688 

98 

666 

67 

58 

667 

363 

887 

664 

932 

9986 

536 

666 

686 

686 

6666 

4965 

594 

563 

439 

357 

6256 

7667 

468 

678 

967 

949 

4949 

6364 

666 

774 

936 

967 

6677 

5635 

546 

668 

866 

842 

6773 

6764 

788 

286 

546 

556 

6758 

7825 

98 

789 

797 

959 

6998 

899 

8 

869 

789 

688 

7957 

9 

Add: 

(7)  89,   966,   878,   696,   788,   966,   787,   989,   89,   95. 

(8)  899,   889,  869,   688,   986,   788,   769,   969,   88,   86. 

(9)  689,   869,   788,   966,   687,  869,  978,  798,  789,  989. 
(10)   899,   998,   866,   689,   969,  789,  669,  898,  678,  668. 


182  ELEMENTARY  ARITHMETIC. 

1.  A  man  starting  on  a  journey  with  $100, 
spends  $87.57;  how  much  has  he  left  ? 

2.  The  sum  of  two  numbers  is  8275,  and  the 
larger  is  4376  ;  what  is  the  smaller  ? 

3.  The  difference  between  two  numbers  is  1565, 
and  the  greater  number  is  9564  ;  what  is  the 
smaller  ? 

4.  A  reader  costs  89  cents,  a  geography  78 
cents,  an  arithmetic  56  cents,  a  slate  17  cents, 
and  a  sponge  5  cents.  If  Albert  works  9  days  at 
37  cents  a  day,  how  much  money  will  he  have  left 
after  paying  for  these  articles  out  of  his  wages  ? 

5.  A.  boy  worked  for  a  farmer  for  6  weeks  at 
$4.38  a  week.  He  spent  $15.75  of  his  wages  for 
a  suit  of  clothes ;  how  much  money  had  he  left  ? 

15.      6  +  9  AND  ICE  view. 

6      16     26      36      46      56      66      76      86     96 
9999999999 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

889 

67 

799 

896 

6 

6 

896 

936 

981 

9695 

65 

963 

986 

194 

616 

5338 

636 

9616 

696 

619 

996 

664 

7464 

7366 

868 

766 

268 

6937 

39 

6987 

769 

759 

399 

9996 

6699 

7586 

996 

996 

663 

6668 

8965 

9936 

897 

399 

567 

977 

8898 

7999 

97 

717 

868 

7196 

8766 

9965 

6 

89 

978 

878 

988 

899 

REVIEW,  183 

1.  A  man  bought  a  house  and  lot  for  $4386, 
and  spent  I  as  much  for  improvements  ;  what  did 
the  property  cost  him  altogether  ? 

2.  A  railroad  train  runs  3003  miles  in  6  days ; 
how  far  is  that  each  day  ?  m 

3.  A  clerk's  salary  is  $675,  of  which  she  uses 
$86  in  the  purchase  of  books,  and  $300  for  board 
and  other  expenses;  how  much  will  she  have 
saved  at  the  end  of  6  years  ? 

4.  How  many  suits  of  clothes  of  6  yards  each 
can  be  made  from  five  pieces  of  cloth,  each  con- 
taining 36  yards  ? 

5.  The  expense  of  a  party  of  6  men  on  a  visit 
to  the  National  Park  was  $1254;  what  was  each 
man's  share  ? 

16.      ORAL  REVIEW. 

1.  At  5  cents  a  yard,  how  much  more  will  8 
yards  of  cloth  cost  than  \\  yards  of  ribbon  at  20 
cents  a  yard  ? 

2.  If  with  $20  you  can  buj^  5  pictures,  how 
many,  at  the  same  rate,  can  you  buy  with  $100? 

3.  A  boy  has  80  cents,  and  spends  1  of  it  for 
marbles;  how  many  blank  books,  at  8  cents  apiece, 
can  he  buy  with  the  rest  of  his  money  ? 

4.  What  will  1  of  a  gallon  of  alcohol  cost,  at  20 
cents  a  pint  ? 


184  ELEMENTARY  ARITHMETIC 

5.  A  man  bought  apples  at  the  rate  of  4  for  3 
cents  and  sold  them  at  the  rate  of  6  for  5  cents ; 
what  did  he  gain  on  24  apples? 

6.  How  many  square  feet  of  surface  in  a  black- 
board 12  feet  long  and  4  feet  wide  ? 

7.  January,  1892,  began  on  Friday.  If  50  cents 
were  paid  into  a  building  association  every  Saturday 
night,  how  much  would  be  paid  that  month  ? 

8.  A  teacher  was  offered  some  pictures  singly 
at  5  cents  apiece,  or  13  for  50  cents ;  what  would 
she  save  by  purchasing  them  all  at  once  ? 

9.  If  14  men  lay  a  track  in  4  weeks,  how  long 
will  it  take  one  man  to  do  the  same  work  ?  How 
long  would  it  take  two  men  ? 

10.  If  5  dozen  eggs  are  worth  $1,  how  many 
cents  are  7  dozen  worth  ? 

11.  My  table  has  a  surface  of  60  square  feet;  if 
it  is  5  feet  wide,  what  is  its  length  ? 

12.  How  many  cubic  inches  in  a  block  of  wood 
which  is  8  inches  long,  4  inches  wide,  and  3  inches 
thick  ? 

17. 

§  are  how  many  wholes  ?  J  -f  ^  =  ?  £  —  £  =  ? 

*■£  are  how  many  wholes  ?  £  +  ^  =  ?  §  —  i  =  ? 

&  are  how  many  thirds  ?  }  +  -ft  =±  ?  1  —  ^  =  ? 

t*V  are  how  many  fifths  ?  £  +  ^  ==  ?  1  —  ^  =  ? 

J  of  J  is  what  part  of  one?  3x|=?  3xf=? 


MULTIPLY  AND  DIVIDE  BY  7. 


185 


18.     Multiply  by  7: 


1.  6948     3.  9485 

5. 

6098 

7.  10769 

2.  5769     4.  7906 

6. 

6937 

8.  11894 

Divide  by  7 : 

1.  19539    4.  39648 

7. 

54957 

10.  17799 

2.  18049    5.  18563 

8. 

13607 

11.  68009 

3.  17825    6.  28359 

9. 

27620 

12.  67265 

19.  1.  If  a  boy  pays  $3.75  for  a  hundred  papers 
and  sells  them  at  5  cents  apiece,  how  much  does 
he  make? 

2.  A  widow  is  to  receive  one  fourth  of  an  es- 
tate of  $16200,  and  the  remainder  is  to  be  divided 
equally  among  five  children ;  what  is  the  share  of 
each  child  ? 

3.  A  book  agent  bought  7  books  at  $3.75  each. 
He  sold  them  at  $6  each.  His  expenses  were 
$6.25.  He  was  unable  to  collect  for  2  books. 
Did  he  gain  or  lose  ?     How  much  ? 

4.  A  flour  merchant  bought  1333  barrels  of 
flour  at  $7  a  barrel.  He  sold  900  barrels  at  $8 
a  barrel,  and  the  remainder  at  $6  a  barrel;  what 
was  his  gain  ? 

5.  Bought  7  cows  at  $37  each,  6  horses  at 
$100  each,  and  250  sheep  at  $4  each.  Sold  all 
for  $2130 ;  what  was  the  gain  ? 


186  ELEMENTARY  ARITHMETIC. 

20.       7+7   AND   REVIEW. 


Read 

endings 

• 

7  \ 

27 

37 

47 

57 

67   77 

87   97 

107 

7 

7 

7 

7 

7 

7   7 

7   7 

7 

(1) 

(2) 

(3) 

w 

(5) 

(6) 

777 

795 

779 

996 

998 

766 

377 

548 

637 

576 

8979 

8735 

747 

877 

765 

455 

6613 

7269 

496 

743 

659 

979 

6267 

7637 

673 

676 

575 

192 

5772 

572 

357 

834 

924 

626 

6386 

9826 

787 

797 

777 

473 

7676 

7466 

774 

272 

565 

856 

8476 

887 

637 

956 

776 

69 

997 

7988 

789 

879 

986 

9 

859 

978 

21. 

SUBTRACTION 

OP  7. 

Read 

endings 

! 

17 

29 

31  ; 

33 

45 

56     74 

62  78  90  86 

7 

7 

7 

7 

7 

7   7 

7   7 

7   7 

Make  tables  subtracting  7  from  numbers  ending 
in  1,  2,  3,  4,  5,  and  6. 
Subtract : 


1.  24442-2456 

2.  13123-1666 

3.  43454-1456 

4.  23455-1666 

5.  35656-4666 

6.  60003-2666 


7.  53320-1777 

8.  44320-2676 

9.  39131-7777 

10.  68442-6767 

11.  49563-6777 

12.  18004-7777 


13.  37464-6476 

14.  18875-3077 

15.  99455-6066 

16.  97563-6767 

17.  19545-6077 

18.  13006-1067 


FACTORS  AND  PRIME  NUMBERS.  187 

1.  Received  during  the  day,  $10.23;  paid, 
$16.83;  on  hand  at  the  close  of  the  day,  $3.55. 
How  much  was  on  hand  at  the  beginning  of  the 
day? 

2.  A  farmer  traded  485  pounds  of  old  iron  at 
3  cents  a  pound  for  a  new  stove  worth  $37.50; 
how  much  cash  should  he  pay  ? 

3.  How  many  years  from  the  landing  of  the 
Pilgrims,  1620,  to  the  Declaration  of  Indepen- 
dence, 1776? 

4.  A  grocer  paid  $12.53  for  prunes,  at  7  cents 
a  pound  ;  how  many  pounds  did  he  buy  ? 

5.  How  much  must  I  add  to  $7650  to  be  able 
to  pay  for  a  farm  worth  $12400  ? 

22.     FACTORS.    PRIME   NUMBERS. 

What  is  a  composite  number  ?  What  is  a  factor 
of  a  number  ?     What  is  an  integer  ? 

1.    Name  the  numbers  which  are  not  composite  : 


1 

6 

11 

16 

21 

26 

31 

36 

2 

7 

12 

17 

22 

27 

32 

37 

3 

8 

13 

18 

23 

28 

33 

38 

4 

9 

14 

19 

24 

29 

34 

39 

5 

10 

15 

20 

25 

30 

35 

40 

A  number  which  has  no  exact  divisor,  except 
itself  and  one,  is  called  a  Prime  Number. 

2.  Write  in  columns  the  numbers  from  40  to  90, 
and  mark  those  that  are  prime  numbers. 


188 


ELEMENTARY  ARITHMETIC. 


A  prime  number  may  be  a  factor  of  some  other 
number. 

3.  What  prime  numbers  are  factors  of  6;  14;  21? 
A  prime   number  used  as  a  factor  is  called  a 

Prime  Factor. 

4.  What  are  the  prime  factors  of  27;  35;  63; 
72? 

5.  Find  all  the  prime  factors  of  108. 

9  x  12  =  108.     9  =  3  x  3,  and  12  =  2  x  2  x  3. 
108  =  3  x  3  x  2  x  2  x  3. 

23.     Find  the  prime  factors  of  280. 

Divide  the  number  by  any 
prime  factor :  if  the  quotient 
is  not  a  prime  factor,  divide 
it  in  the  same  way.  Con- 
tinue to  divide  until  the  quo- 
tient is  a  prime  number.  The 
divisors  and  the  last  quotient 
are  the  prime  factors. 


7)280 

5)40 

2)_8 

2)4 

2 

7x5x2x2x2  =  280 

Prime  factors. 


Find  prime  factors : 

1.  210    4.  312    7.  546 

2.  287    5.  390    8.  594 

3.  246   6.  486   9.  684 


10.  615   13.  873 

11.  714    14.  910 

12.  819    15.  987 


24.   7  +  8  AND  REVIEW. 

Read  endings : 

7      27      37      47      57      67      77      87      97      107 
888888888         8 


HE  VIEW. 


189 


(1) 

888 
777 
443 
978 
726 
789 
621 
775 
647 
689 


(2) 
888 
382 
627 
365 
967 
194 
797 
777 
949 
589 


(3) 

778 
223 
879 
458 
764 
228 
977 
842 
498 
798 


(4) 
669 
179 
768 
795 
987 
876 
754 
478 
729 
978 


(5) 

789 

6846 

7973 

4769 

6268 

8666 

9568 

7599 

975 

89 


(6) 

6789 

6677 

9826 

3667 

9547 

6978 

8779 

978 

74 

9 


25.  Subtract : 

1.  44320-1667    5.  69676-5767 

2.  36543-4757    6.  49075-7076 

3.  17654-5667    7.  29640-6777 

4.  28065-6776   8.  90653-3767 


9.  80076-2076 

10.  70604-5075 

11.  60243-4767 

12.  59456-7537 


1.  A  lady  had  $30.  She  bought  a  dress  for 
$8.10,  shoes  for  $1.85,  7  yards  of  cashmere  at 
75  cents  a  yard,  and  a  shawl  for  $4 ;  how  much 
had  she  left  ? 

2.  A  merchant  buys  boots  at  $5.20  a  pair,  and 
sells  them  at  $6  a  pair;  what  does  he  make  in 
selling  7  pairs  ? 

3.  My  grocery  bill  on  the  several  days  of  the 
week  was  $3.76,  $2,  $3.58,  $2.07,  $1.89,  and 
$1.45.  On  this  I  paid  at  one  time  during  the 
week  $5,  and  at  another  $4.50;  how  much  do  I 
still  owe  ? 

4.  How  much  more  will  7  yards  of  cloth  cost,  at 
$4.50  per  yard,  than  5  yards  at  $3.75  per  yard? 


190  ELEMENTARY  ARITHMETIC. 

26.      7  +  9    AND    REVIEW. 

Read  endings  : 

7     17    27     37     47     57     67     77     87     97     107 
9999999999         9 


—  — 



(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(?) 

999 

977 

988 

789 

794 

9779 

97 

776 

296 

979 

189 

9685 

9979 

686 

245 

872 

777 

756 

8546 

6877 

399 

777 

187 

448 

257 

8767 

6777 

769 

833 

956 

776 

764 

6794 

864 

267 

999 

797 

129 

657 

9467 

6468 

988 

632 

427 

794 

775 

1895 

9736 

233 

769 

984 

669 

867 

8736 

798 

777 

647 

227 

778 

978 

6759 

9797 

97 

789 

898 

976 

598 

988 

986 

89 

27. 

Subtract : 

1. 

38345 

-  14677 

4. 

20412  - 

-7777 

7.  17653-2767 

2. 

39745 

-  16756 

5. 

10586  - 

-  5767 

8.  69114-7116 

3. 

10000 

-  6117 

6. 

70001  - 

-4006 

9.  80000-   67 

28.      ORAL    REVIEW. 

1.  f  of  21  +  1  of  40  are  how  many  times  6  ? 

2.  Bought  6  bars  of  soap  for  a  quarter  of  a  dol- 
lar ;  how  much  is  that  a  bar  ?  What  will  9  bars 
cost  at  the  same  rate  ? 

3.  James  had  72  cents.  He  spent  \  of  it  for  a 
new  book,  and  \  for  pencils  ;  what  part  did  he 
spend  ?    What  part  has  he  left  ?    How  many  cents  ? 

4.  A  colt  was  bought  for  $60,  and  sold  for  \\ 
times  its  cost ;  what  was  the  gain  ? 


REVIEW.  191 

5.  What  will  f  of  35  pears  cost  at  5  cents  each  ? 

6.  What  will  1  of  a  gallon  of  vinegar  cost  at  9 
cents  a  quart  ? 

7.  A  market  woman  bought  4  quarts  of  berries 
for  39  cents,  and  sold  them  at  6  cents  a  pint;  how 
much  did  she  gain  ? 

8.  How  many  minutes  in  i|  of  an  hour  ?  What 
other  part  of  an  hour  can  we  call  this? 

9.  At  the  rate  of  7  marbles  for  9  cents,  what 
will  3|  dozen  cost  ?     3|  dozen  is  how  many  times  7  ? 

10.  I  have  66  cents.  If  I  spend  n  of  them  for 
eggs,  how  many  will  I  get  at  24  cents  a  dozen?  If 
I  then  spend  n  of  the  whole  number  for  a  pound  of 
butter,  what  part  of  my  money  have  I  left  ?  If  I 
then  spend  1  of  the  remainder  for  nuts,  how  much 
money  have  I  left? 

11.  If  12  cents  is  \  of  the  cost  of  a  book,  what 
will  2  books  cost  ? 

12.  At  7  cents  an  ounce,  what  will  3|  pounds  of 
nutmegs  cost? 

13.  A  grocer  buys  8  barrels  of  apples,  7  times 
that  number  of  barrels  of  potatoes,  and  \  as  many 
barrels  of  turnips  as  potatoes.  How  many  barrels 
of  turnips  does  he  buy  ? 

14.  Frank  had  $2.80.  He  spent  \  of  it  for  a 
cap,  \  of  it  for  a  ball,  and  with  the  remainder 
bought  a  book ;  how  much  did  the  book  cost  ? 


192  ELEMENTARY  ARITHMETIC. 

15.  If  7  yards  of  cloth  cost  $53,  for  how  much 
must  it  be  sold  a  yard  to  gain  $10? 

16.  A  man  bought  56  pounds  of  sugar  and  sold 
\  of  it ;  how  many  pounds  has  he  left  ? 

17.  I  had  70  cents.  Of  this  I  spent  \  for  some 
cheese,  and  f  for  steak ;  how  many  sevenths  had  I 
left  ?     How  much  money  ? 

18.  If  7  yards  of  ribbon  cost  $4.20,  what  should 
2  yards  cost  ? 

19.  A  dealer  had  77  baskets  of  cranberries. 
11  baskets  were  spoiled;  what  part  of  his  cran- 
berries were  good  ? 

29. 

■£$  are  how  many  fourths  ?  $  -f  J  =  ?  j_j=? 

£$  are  how  many  fourths  ?  J  +  £  =  ?  J  —  £  =  ? 

££  are  how  many  fifths  ?  £  +  £  =  ?  8xf=? 

iJ  are  how  many  tenths  ?  J  —  i  =  ?  7  X  f  =  ? 

30.   Multiply  by  8: 

1.  3849    3.  6957    5.  6384    7.  6094    9.  8649 

2.  8539    4.  9384    6.  3947    8.  7483    10.  5973 


Divide  by  8 : 

1.  41443   3.  56457 

5.  21391 

7.  29019 

9.  62808 

2.  51652   4.  58259 

6.  39036 

8.  78863 

10.  39013 

31.  1.  At  $2.40  a  gallon,  what  is  the  price  of 
a  pint  of  varnish  ? 

2.  How  many  two-gallon  pails  will  be  required 
to  hold  64  quarts  of  water  ? 


REVIEW.  193 

3.  One  man  can  build  a  wall  in  120  days ;  how 
long  will  it  take  8  men  to  do  it  ? 

4.  At  $8  a  head,  how  many  sheep  can  be  bought 
for  $552  ? 

5.  At  $1.60  a  bushel,  what  is  1  quart  of  straw- 
berries worth  ? 

6.  A  coal  dealer  paid  $1752  for  coal  at  $8  a 
ton ;  how  many  tons  did  he  buy  ? 

7.  How  many  barrels  of  flour  at   $8  a  barrel 
will  pay  for  52  cords  of  wood  at  $6  a  cord  ? 

32.      8  +  8  AND  KEVIEW. 


(1) 

(2) 

(3) 

W 

(5) 

(6) 

(?) 

787 

698 

988 

878 

378 

97 

77 

439 

797 

675 

636 

889 

7719 

9998 

978 

685 

799 

987 

386 

8778 

8794 

828 

878 

479 

957 

879 

8653 

7347 

584 

154 

988 

969 

787 

4877 

5865 

748 

488 

843 

768 

687 

7777 

7179 

886 

728 

788 

856 

995 

4859 

2759 

686 

871 

788 

949 

297 

8796 

9578 

738 

348 

919 

786 

798 

89 

628 

988 

899 

899 

877 

768 

7 

88 

33.    Subtraction  of  8  : 
Read  endings : 

11    23    38    44    50    62    75    87    99    96    101 
8      8_8_8_8_8_8_8      8      8        8 

Make  tables,  subtracting  8  from  numbers  ending 
in  1,  2,  3,  4,  5,  6,  and  7. 

13E 


194  ELEMENTARY  ARITHMETIC. 

Subtract: 

1.  24321-2878  5.  29530-  4878  9.  20595-  5468 

2.  16653-  388  6.  14878-  7807  10.  60677-  6878 

3.  37304-5888  7.  88676-17878  11.  69004-10768 

4.  48765-4878  8.  19644-  888  12.  78002-  7834 

34.  1.  A  lady  bought  2  yards  of  ribbon  at 
37  cents  a  yard,  6  yards  of  muslin  at  19  cents  a 
yard,  3  yards  of  flannel  at  35  cents  a  yard,  5  yards 
of  lace  at  98  cents  a  yard,  some  needles  for  31 
cents,  and  a  belt  for  75  cents ;  what  did  her  pur- 
chases amount  to  ? 

2.  Bought  a  pair  of  boots  for  $8.50,  an  umbrella 
for  $3.62,  a  pair  of  gloves  for  $1.25,  some  collars 
for  $0.75,  and  a  hat  for  $4  ;  what  did  all  cost  ? 

3.  Bought  8  yards  of  velvet  at  $1.25,  4  yards 
of  satin  at  $1.85,  6  yards  of  Spanish  lace  at  $0.87, 
and  7  yards  of  sateen  at  $0.38.  Make  out  the 
bill. 

4.  Mr.  John  R.  Holt  bought  of  Hains  &  Co., 
6  dozen  oranges  at  28  cents  a  dozen,  4  pounds  of 
tea  at  75  cents  a  pound,  8  lamp  chimneys  at  10 
cents  each,  10  pounds  of  crackers  at  9  cents  a 
pound,  5  pounds  of  coffee  at  35  cents  a  pound,  and . 
8  pounds  of  starch  at  20  cents  a  pound.  Make  out 
the  bill. 

5.  One  third  the  value  of  my  farm  is  \  the  value 
of  my  house  and  lot.  If  the  farm  is  worth  $3600, 
what  is  the  value  of  the  house  and  lot  ? 


8  +  9  AND  REVIEW.  195 

35.       8+9    AND    REVIEW. 

Read  endings  : 
8      18      28      38      48      58      68      78      88      98 
9999999999 

1.  Add  899,  283,  998,  158,  895,  887,  728, 
993,  947,  989. 

2.  Find  the  sum  of  78,  8887,  9988,  9763,  8989, 
8799,  95,  9887,  48,  988. 

3.  Add  767,  6512,  9899,  8269,  768,  6938, 
9799,  8967,  937,  8788. 

4.  Find  the  amount  of  89,  6478,  9878,  7468, 
9826,  9676,  9832,  7989,  899,  7. 

5.  679  +  695  +  977  +  889  +  649  +  877  +  778 
+  898  +  879  +  879  =  ? 


36. 

(i) 

(2) 

(3) 

W 

(5) 

(6) 

(?) 

899 

8 

9 

78 

767 

89 

679 

283 

839 

979 

8887 

6512 

6478 

695 

998 

888 

83 

9988 

9899 

9878 

977 

158 

889 

848 

9763 

8269 

7468 

889 

895 

393 

889 

8989 

768 

9826 

649 

887 

868 

738 

8799 

6938 

9676 

877 

728 

474 

996 

95 

9799 

9832 

778 

993 

987 

897 

9887 

8967 

7989 

898 

947 

859 

58 

48 

937 

899 

879 

989 

79 

69 

988 

8788 

7 

879 

196 


ELEMENTARY  ARITHMETIC. 


37. 

Multiply  by  9 

1. 

8439 

6.  5968 

11. 

6874 

16.  9005 

21  6298 

2. 

7095 

7.  6374 

12. 

3758 

17.  8161 

22.   2759 

3. 

6394 

8.  4738 

13. 

8647 

18.  7463 

23.  8463 

4. 

8007 

9.  6834 

14. 

9376 

19.  6389 

24.  3874 

5. 

6398 
Divide 

10.  4958 
iby9: 

15. 

4837 

20.  8476 

25.  6438 

L 

15443 

7.  13540 

13. 

3912$ 

19.  53080 

25.  29123 

2. 

17867 

8.  44547 

14. 

29109 

20.  44064 

26.  20367 

3. 

27364 

9.  88432 

15. 

24389 

21.  41229 

27.  23389 

4. 

72351 

10.  76302 

16. 

66093 

22.  45562 

28.  35198 

5. 

11128 

11.  68134 

17. 

75623 

23.  89054 

29.  55555 

C. 

55408 

12.  47562 

18. 

64224 

24.  76323 

30.  44444 

38.  1.  How  many  square  yards  in  90  square 
feet? 

2.  What  is  the  cost  of  18  square  yards  of  can- 
vas, at  8  cents  a  square  foot  ? 

3.  Name  the  numbers  divided  by  9  which  give 
the  following  results :  8,  11,  7,  12,  6,  9. 

4.  What  will  2|  bushels  of  strawberries  cost,  at 
9  cents  a  quart  ? 

5.  A  clerk  saved  $114.66  in  9  months ;  his 
salary  was  $75  a  month  ;  what  were  his  expenses 
each  month  ? 

6.  If  I  buy  9  horses  at  $120  each,  and  sell  all 
of  them  for  $2000,  how  much  do  I  gain  ? 


SUBTRACTION  OF  9. 
39.       9  +  9. 


197 


Read  endings  : 
9       19      29      39      49      59      69      79      89      99 
'LJLl.l.JLl.jtll-l. 

Add: 

(1)  9998,  6799,  8798,  9789,  8989,  9987,  8899,  7899, 
7027,  698. 

(2)  7978,  5887,  7646,  9687,  9596,  6988,  8799,  7996, 
7968,  967. 

40.  SUBTRACTION  OF  9. 

Read  endings  : 
11      43      28      32      54      65      79      87     96     109 
A     .1     .1      1.      1      1      111-J*. 

Subtract : 

1.  88764-   2969  6.  40031-   9594  11.   10962-   2999 

2.  49875-   2789  7.  58431-   3989  12.   68753-    9095 

3.  37953-   1896  8.  19052-   9298  13.   90087-    5069 

4.  90585-13898  9.  90745-11989  14.   19864-10989 

5.  60103-     389  10.  70001-   9867  15.   90003-    7648 

41.       MISCELLANEOUS    PROBLEMS. 

1.  9  rugs,  which  cost  $7.80  each,  were  sold  for 
$85.41 ;  what  was  the  profit  on  each  rug  ?  On  9 
rugs  ? 

2.  A  merchant  bought  9  pieces  of  merino,  each 
piece  containing  45  yards.  After  selling  135  yards, 
how  many  dress  patterns  of  9  yards  each  had  he 
left? 


198  ELEMENTARY  ARITHMETIC. 

3.  A  laborer  saves  $9  a  month ;  how  many 
months  will  it  take  him  to  save  $684  ?  How 
many  years  ? 

4.  Bought  882  acres  of  woodland.  After  clear- 
ing  one  ninth  of  it,  I  sold  the  cleared  land  at  $8 
an  acre  and  the  woodland  at  $9  an  acre;  how 
much  did  I  receive  in  all  ?  t 

5.  If  you  have  $238  when  you  are  18  years 
old,  and  save  $49  each  year  until  you  are  27,  how 
much  money  will  you  then  have  ? 

6.  A  lady  having  $125,  bought  a  cloak  for  $75, 
and  7  yards  of  silk  at  $1.85  a  yard  ;  how  much 
money  had  she  left? 

7.  A  coal  dealer  bought  11  tons  of  coal  for 
$144.97  and  sold  it  at  $8.50  a  ton;  did  he  gain 
or  lose  ?     How  much  ? 

8.  One  piece  of  muslin  is  9  cents  a  yard,  and 
another  is  6  cents  a  yard;  if  I  have  $1.80,  how 
many  more  yards  of  the  second  kind  can  I  buy 
than  of  the  first  ? 

9.  A  hotel-keeper  bought  98  pounds  of  crackers 
at  8  cents  a  pound,  and  138  loaves  of  bread  at  6 
cents  a  loaf ;  how  much  did  he  pay  for  both  ? 

10.  At  5  cents  a  quart,  what  is  the  value  of  a 
barrel  of  cider  containing  311  gallons  ? 

11.  Sold  567  barrels  of  flour  for  $9  a  barrel; 
the  wheat  cost  $2795,  the  expense  of  milling  was 
$670;  how  much  was  gained? 


NOTATION  AND  NUMERATION.  199 

CHAPTEE    III. 
1.     NOTATION  AND   NUMERATION. 

TWO    PERIODS:    UNITS    AND    THOUSANDS. 

2d  period.    1st  period. 
Thousands.      Units. 


Ill         111 

000     000 

Ten  ten-thousands  are  equal  to  one  hundred- 
thousand. 

One  hundred-thousand  is  how  many  times  ten 
thousand  ? 

Hundred-thousands  are  written  in  the  first  place 
to  the  left  of  ten-thousands. 

352,400  is  read,  three  hundred  fifty-two  thou- 
sand four  hundred.  The  figure  3  expresses  the 
number  of  hundred-thousands. 

Expressing  numbers  by  means  of  figures  is 
called  Notation.  Expressing  in  words  a  number 
written  in  figures  is  called  Numeration. 

Ten  units  of  any  order  make  one  of  the  next 
higher  order. 

In  the  number  405,623,  in  what  place  or  order 
does  the  figure  6  stand  ?    The  figure  4  ?    2  ?    0  ? 


200  ELEMENTARY  ARITHMETIC. 

2.  Write  6  ciphers  and  separate  them  into 
periods.  Place  3  in  hundred-thousands'  place, 
2  in  thousands'  place,  and  4  in  hundreds'  place. 
Read  the  number  you  have  written. 

Read  the  following  numbers  : 


401,392 

500,020 

800,005 

110,111 

503,001 

909,008 

850,050 

101,001 

648,406 

763,204 

616,016 

111,101 

Express  the  following  in  figures : 

Two  hundred  thousand  sixty-three. 
Seven  hundred  seven  thousand  eighty-one. 
Five  hundred  fifty-one  thousand  one. 
Eight  hundred  eighteen  thousand  six. 
One  hundred  eleven  thousand  eleven. 
Two  hundred  thousand  twelve. 
Nine  hundred  nineteen  thousand  nineteen. 

3.     THREE    PERIODS:     UNITS,   THOUSANDS,   AND 
MILLIONS. 

3d  period.    2d  period.    1st  period. 
Millions.    Thousands.       Units 

-5      "      -3 

Bee 

a*.-    a"-    c»"3 

111   1 1  §   111 

000  000  000 

The  third  period  of  figures  expresses  ones  of  mil- 
lions, tens  of  millions,  and  hundreds  of  millions. 

Write  9  ciphers  and  separate  them  into  periods 
Place  3  in  ten-thousands'  place,  6  in  ten-millions' 


MULTIPLYING  AND  DIVIDING   BY  10.        201 

place,  8  in  tens'  place,  4  in  thousands'  place,  and 
7  in  millions'  place.     Read  the  number. 

4>    Read  the  following  numbers  : 

100,000,000  150,004,150  19,300,019 

1,000,000  50,040,040  9,999,000 

4,700,630  804,307,321  11,110,011 

20,343,101  10,010,001  10,111,101 

Write  in  figures  : 

Fifty-six  million  one  hundred  seventeen  thou- 
sand six  hundred  nine. 

Three  hundred  eight  thousand  three  hundred 
eight ;    six  million   sixteen. 

Ten  million  one  hundred  eleven  thousand  one 

5.     MULTIPLYING   AND   DIVIDING   BY   10. 

Find  products : 

7865  x  10       8079  x  10        80563  X  10        96532  x  10 

Short  Method.  When  the  multiplier  is  10,  the  product 
is  obtained  by  annexing  zero  to  the  multiplicand. 

89736  x  10       78895  x  10       45838  x  10       40009  x  10 

Find  quotients : 

28930  ^  10      26845  + 10     870470  -=- 10     693879  -4- 10 

Short  Method.  Cut  off  one  figure  from  the  right  of  the 
dividend.  The  remainder  will  be  the  figure  cut  off  from 
the  dividend. 

7630456  -f- 10     3987652  +  10     3101487  ~- 10 


202 


ELEMENTARY  ARITHMETIC. 


6.     MULTIPLYING   AND   DIVIDING   BY    11. 

TABLES. 

10  x  11  =  HO  11  X  11  =  121  12  X  11  =  132 

Copy  the  following,  and  complete  to  12  x  11  =  132 
and  132-11  =  12. 


0x11=   0 
1  x  11  =  11 


2  x  11  =  22 

3  x  11  =  33 


11-11  =  1  16-7-11  =  1,  5rem.  21 

12-11  =  1,  1  rem.  17-11  =  1,  6  rem.  22- 

13-11  =  1,  2 rem.  18-11  =  1,  7 rem.  23 

14-11  =  1,  3rem.  19+11  =  1,  8  rem.  24 

15-11  =  1,  4rem.  20-11  =  1,  9 rem.  25 


Multiply  by  11 : 

1.  89723    3.  830976 

2.  65049    4.  394857 

Divide  by  11 : 

1.  25S26        4.  899604 

2.  20441    5.  283563 

3.  37838   6.  190009 


5.  385047 

6.  629875 


4  x  11  =  44 

5  x  11  =  55 

-11  =  1,  10  rem. 
•11  =  2 

-11  =  2,  lrem. 
-11=2,  2  rem. 
-11  =  2,  3  rem. 


7.  748693 

8.  480019 


7.  567802    10.  9800457 

8.  900456    11.  2394836 

9.  404040    12.  1938479 


7.   ORAL  REVIEW. 

1.  A  man  bought  a  horse  for  $64.  He  paid  |  of 
the  cost ;  how  much  does  he  still  owe  ? 

2.  A  farmer  having  96  bushels  of  apples  sold 
|  of  them,  used  |,  and  stored  the  remainder;  how 
many  bushels  were  stored  ? 


REVIEW.  203 

3.  In  how  many  days  can  6  men  do  as  much 
work  as  8  men  can  do  in  9  days  ? 

4.  If  8  barrels  of  flour  cost  $58,  and  were  sold 
at  $8  a  barrel,  what  was  the  gain  ? 

5.  If  a  boy  earns  $8  a  month,  and  spends  |  of 
his  wages  for  clothes,  how  much  will  he  save  in  a 
year  ? 

6.  A  man  gave  80  cents  for  his  lodging,  which 
was  f  as  much  as  his  meals  cost ;  how  much  did 
his  meals  cost? 

7.  9x7  +  9  divided  by  12  is  what  part  of  36  ? 

8.  A  man  had  96  books  and  sold  84  of  them ; 
what  part  of  his  books  had  he  left  ? 

9.  If  9  yards  of  muslin  cost  108  cents,  what 
will  7  yards  cost  ? 

10.  A  man  paid  75  cents  for  his  lodging,  which 
was  |  of  the  cost  of  his  meals ;  what  were  his  ex- 
penses for  the  day  ? 

11.  If  12  yards  of  cloth  cost  $86,  for  how  much 
per  yard  must  it  be  sold  to  gain  $10  ?     $16  ? 

12.  At  9  cents  a  yard,  how  much  more  will  9 
yards  of  ribbon  cost,  than  2|  yards  at  21  cents  a 
yard  ? 

13.  A  boy  started  to  the  show  with  $5.00.  He 
paid  \  of  it  for  a  railroad  ticket,  |  of  the  remainder 
for  his  dinner,  1  of  what  was  left  for  bananas,  }  of 
what  then  remained  for  a  ticket  to  the  show.  How 
much  had  he  left  ? 


204  ELEMENTARY  ARITHMETIC. 

14.  If  a  cook  uses  9  eggs  each  day,  in  how 
many  days  will  she  use  9  dozen? 

15.  A  horse  is  worth  $144,  but  a  man  wishing 
to  buy  it  has  only  $96.  How  many  more  dollars 
must  he  have  to  buy  the  horse  ? 

16.  A  man  has  $81.  He  paid  |  of  it  for  a  pony 
and  I  for  a  cart ;  what  part  of  his  money  did  he 
spend  ?  What  part  did  he  have  left  ?  How  much 
money  did  he  spend  ? 

17.  Howr  many  squashes  at  7  cents  each  will 
pay  for  91  pounds  of  prunes  at  9  cents  a  pound  ? 

8#    4  of  £  is  what  part  of  a  whole  ? 
J  of  J  is  what  part  of  a  whole  ? 

*  +  *  =  ?         i  +  i  =  ?         i+.*-* 
J  of  J  of  a  yard  is  how  many  inches  ? 
J  of  J  of  a  yard  is  how  many  inches  ? 

1.  If  $9185  be  equally  divided  among  11  men, 
how  many  dollars  will  each  receive  ? 

2.  A  merchant  bought  11  pieces  of  alpaca  of  39 
yards  each.  After  selling  119  yards  how  many 
dress  patterns  of  10  yards  each  has  he  left  ? 

3.  The  product  of  two  numbers  is  40128 ;  one 
of  the  numbers  is  11,  what  is  the  other  ? 

4.  How  many  days  in  11  years  ? 

5.  A  shoe  merchant  made  $240.90  on  11  dozen 
pairs  of  shoes ;  what  was  the  profit  on  one  dozen 
pairs  ? 


OPERATIONS   WITH  12. 


205 


9.     MULTIPLYING    AND    DIVIDING    BY    12. 

TABLES. 

9X12  =  108     10x12  =  120      11x12  =  132     12x12  =  144 

Copy    the    following    tables,    and    complete    to 
12  x  12  and  144  -  12. 


0  x  12  =  0 

1  X  12  =  12 


2  x  12  =  24 

3  x  12  =  36 


4  x  12  =  48 

5  x  12  =  60 


12+12  = 


13- 
14- 
15 
16 


12: 

12: 
12: 
12: 


17-5-12  = 


1  18+12 

1,  lrem.  19+12 

1,2  rem.  20+12 

%  3  rem.  21  +  12 

1,4  rem.  22+12 

1,  5  rem.  23+12 


Find  products : 


1.  7809  X 

2.  9489  X 

3.  7618  X 

4.  9284  X 


12  5.  29848X12 

12  6.  729521  X  12 

12  7.  47836  X  12 

12  8.  39647X12 


=  1,    6  rem.  24+12  =  2 

=  1,    7  rem.  25+12  =  2,  1  rem. 

=  1,    8  rem.  26  +  12  =  2,  2  rem. 

=  1,    9  rem.  27+12  =  2,  3  rem. 

=  1,  10  rem.  28  +  12  =  2,  4  rem. 

=  1,  11  rem.  29+12  =  2,  5  rem. 


9.   637498  X  12  13.  618094  X  12 

10.  349526X12  14.   190728X12 

11.  67849X12  15.728397X12 

12.  569003X12  16.  855356X12 


Divide  by  12 : 


1.  6384 

2.  2952 

3.  29548 

4.  98345 

5.  54389 

6.  87432 


7.  49673 

8.  83440 

9.  970836 

10.  483974 

11.  298375 

12.  483762 


13.  78645321 

14.  11111111 

15.  99999999 

16.  35689031 

17.  24949678 

18.  86078593 


19.  986000487 

20.  758192436 

21.  967689363 

22.  689285349 

23.  478690007 

24.  692746583 


206  ELEMENTARY   ARITHMETIC, 

10.       MISCELLANEOUS    PROBLEMS. 

1.  A  manufacturer  received  $2688  for  gloves, 
at  the  rate  of  $12  per  dozen  pairs;  how  many 
dozen  pairs  did  he  sell  ? 

2.  A  man  left  a  fortune  of  $3917502  to  his 
wife,  5  children,  and  3  brothers;  what  is  the  share 
of  each,  if  the  money  be  equally  divided  ? 

3.  How  many  tons  of  coal,  at  $9  per  ton,  can  be 
bought  for  $3785904  ? 

4.  How  many  barrels  of  flour,  at  $9  per  barrel, 
will  pay  for  60  cords  of  wood,  at  $12  per  cord  ? 

5.  12  men  can  do  a  piece  of  wrork  in  20  weeks, 
counting  6  working  days  to  the  week;  in  how 
many  days  can  one  man  do  the  same  work  ? 

6.  How  many  revolutions  will  be  made  by  a 
wheel  12  feet  in  circumference  in  running  52800 
feet? 

11.    MISCELLANEOUS   TABLES. 
NUMBERS.  PAPER. 

12  things  are  1  dozen.  24  sheets  are  1  quire. 

12  dozen  are  1  gross.  20  quires  are  1  ream. 

20  things  are  1  score.  2  reams  are  1  bundle. 

A  bushel  of  wheat,  potatoes,  or  beans  =  60  lb, 

A  bushel  of  corn  or  rye  =  56  lb. 

A  bushel  of  corn-meal,  rye-meal,  or  cracked  corn  =  50  lb 
A  bushel  of  barley  =    48  lb. 

A  bushel  of  timothy        =    45  lb. 
A  bushel  of  oats  =    32  lb. 

A  barrel  of  flour  =  196  lb. 

L  barrel  of  beef  or  pork  =  200  lb. 


BILLS. 


207 


12.    BILLS. 

1.    Bought  25  lb.  of  sugar,        @ 

"  If    V  . 

.  $ 

it 

11      "     tea,            « 

48  f    .    . 

u 

12      "      coffee,        « 

530     .     . 

u 

22      «      raisins,       " 

11^    .     . 

u 

19      "      currants,    " 

9  ^     .     . 

u 

18      "      crackers,    " 
the  amount  of  my  bill  ? 

12/  \    . 

What  is 

2.    Bought  12  lb.    of  dried  apples,  @    9  <P     . 

.$ 

a 

14  doz.  "  eggs,  * 

"  15  f    . 

a 

32  qt.    "  milk, 

"      6/  ;    . 

it 

9  bu.    "  potatoes, 

"  65  f    . 

ti 

12  1b.     "  butter, 

"  22f     . 

u 

11  lb.    "  cheese, 
the  amount  of  my  bill  ? 

"  18  ^     . 

What  is 

3.    Bought    9  bbls.  of  apples       @  $2.15     . 

.  $ 

(( 

12  bu.      u  plums 

"     1.20    . 

it 

9  "       "  peaches 

«     1.75     . 

u 

20  "       "  cherries 

*     1.05     . 

it 

12   "       «  pears 

*     1.35    . 

a 

11    "        "  quinces 

«     1.50     . 

What  was  the  whole  amount  ? 


4.  Cincinnati,  O.,  Aug.  27,  1890. 

Mr.  John  Norris, 

Bought  of  Charles  E.  Scott  &  Co., 
3  student  lamps                    @  $ 3.75     .     .     .     .  $ 
1  doz.  knives  and  forks        "     4.25     .... 
1  doz.  plated  teaspoons         "     2.65     .... 
1  refrigerator 12.75 

1  lawn  mower 6.10 

2  rakes,  $0.68  and  $ 0.93 

1  step  ladder 4.75 

Eeceived  payment, 

CHARLES  E.  SCOTT  &  CO 
per  John  M.  Austin. 


208 


ELEMENTARY  ARITHMETIC. 


5.  Cincinnati 
Mr.  James  K.  Martin, 

Bought  of  Lloyd,  Watson  &  Co., 

9  yards  of  cassimere,  @  $2.85     .     .     . 

12  yards  of  pressed  flannel,  "       .58     .     .     . 

11  yards  of  black  silk,  "     1.65     .     .     . 

2  pairs  of  hose,  "       .75,  $1.25  . 


0.,  Aug.  27,  1892. 


lcL_ 

loak 

18.00 

1  pair  of  blankets 

6.75 

6  handkerchiefs, 

"   .40 

9  li 

nen  towels, 

Received 

"   .35 
payment, 

.  .  . 

LLOYD, 

WATSOE 
W. 

[  &  CO 

13. 

Add: 

(i) 

(2) 

(3) 

W 

(5) 

(6) 

(7) 

(8) 

28 

88 

38 

56 

29 

28292 

13977 

44189 

92 

32 

89 

<69 

99 

94919 

88945 

99899 

19 

99 

93 

95 

92 

98189 

98288 

65288 

81 

88 

38 

56 

29 

28922 

33947 

76879 

28 

33 

89 

69 

99 

94889 

89885 

88968 

92 

89 

93 

95 

92 

98328 

99689 

47399 

19 

98 

38 

56 

29 

28994 

33641 

89863 

81 

33 

89 

69 

99 

94418 

98888 

6625H 

28 

89 

93 

95 

92 

98999 

88697 

98898 

92 

91 

38 

56 

29 

28884 

33635 

75364 

19 

38 

89 

69 

99 

94937 

89889 

84959 

81 

99 

93 

95 

92 

98488 

99398 

66895 

28 

83 

38 

56 

29 

28992 

33533 

78386 

92 

39 

S8 

69 

99 

94838 

88489 

95939 

19 

83 

95 

94 

95 

89985 

98982 

58897 

J? 

95 

74 

74 

73 

76794 

87696 

89661 

Subtract : 

1.   1000101 

— 

34587G 

> 

4.  90148003  - 

9876435 

2.  80118181 

— 

698197 

5.   67100011  - 

400968 

3.  864121133 

-  36849762 

► 

6.  810890890- 

209870*9 

LONG   DIVISION. 


209 


14.     TO   MULTIPLY  WHEN  THE  MULTIPLIER  CON- 
SISTS   OF   MORE   THAN   ONE   ORDER. 


Multiply  968  by  18 


968 
18 
8  times  968  =    7744  1st  partial  product. 
10  times  968  =    9680  2d  partial  product. 
18  times  968  =  17424  total  product. 

The  product  of  968  units  by  8  units  gives  7744  units. 
The  product  of  968  units  by  1  ten  gives  968  tens   (9680 
units). 

7744  units  +  968  tens  =±  17424  units. 

Note.  It  is  not  necessary  to  write  the  zero  as  the  right-hand  figure  of 
the  second  partial  product.  The  product  of  8  units  by  1  ten  is  80,  and  the 
8  tens  must  be  written  in  tens'  piace,  in  the  partial  product. 

15.    Find  products : 

1.  70G97  X  26   7.  78009  X  95  13.  10086  X  97  19.  30085  X  68 

2.  68309  X  58   8.  87926  X  87  14.  28594  X  85  20.  46927  X  74 
3.13597X94   9.90193X68  15.39457X69  21.37619X40 

4.  24318  X  68  10.  29658  X  76  16.  53749  X  58  22.  46538  X  87 

5.  37906X47  11.  19037X98  17.  94008X37  23.  90108X90 

6.  56708  X  89  12.  78395  X  79  18.  58096  X  59  24.  18693  X  88 

16.     LONG   DIVISION. 


Divide  2688  by  12  : 

Short  Method. 

Long  Method. 

12  )  2688 

224  quotient. 

12)2688(224  quotient. 
24 

28 

24 

48 

48 

14E 


Partial 
dividends. 

Partial 
quotients. 

2400 

200 

240 

20 

48 

4 

2688 

224  quotient. 

210  ELEMENTARY  ARITHMETIC. 

2600  contains  12  two  hundred  times,  with  2  hundreds 
remaining  undivided. 

28  tens  contains  12  two  tens  times,  with  4  tens  remain- 
ing undivided. 

48  units  contains  12  four  times. 


12 


The  process  of  Long  Division  is  the  same  as 
that  of  Short  Division,  except  that  the  work  is 
written  in  full,  and  the  quotient  is  written  to 
the  right  of  the  dividend. 

Find  quotients : 

Find  the  quotient  figure  by  using  the  left-hand  figure  of 
the  divisor  as  a  trial  divisor. 

1.  3840  -r- 12  7.  3453^  15  13.3800^18  19.    6120 -r- 18 

2.1456^13  8.  6720 -*- 12  14.4370^-19  20.    7989-19 

3.  2899 -M  3  9.6820-12  15.5304-^-17  21.    8600-^19 

4.  4686  -h  22  10.  4480  -h  14  16.  5990  ^  17  22.  31688  -i-  24 

5.  2825  H-  25  11.  3682  -^  16  17.  4000  -h  16  23.  79572  -~  36 

6.  4899  4-  23  12.  3800  -^  17  18.  4600  -i- 19  24.  95040  -i-  45 

17.  MISCELLANEOUS  PROBLEMS. 

1.  How  much  can  I  save  in  a  year  if  I  earn  $140 
each  month  for  ten  months,  and  spend  $68.63  each 
month  for  12  months  ? 

2.  What  will  2  bushels  of  berries  cost  at  12 1 
cents  a  quart  ? 


MISCELLANEOUS  PROBLEMS.  211 

3.  A  man  bought  28  boxes  of  lemons  at  $5.25 
per  box,  and  sold  them  at  $4.68  per  box;  how 
much  did  he  lose? 

4.  How  many  cubic  inches  in  a  block  of  wood  12 
inches  long,  12  inches  wide,  and  12  inches  high  ? 

5.  If  I  save  5  cents  a  day,  how  much  shall  I 
save  in  19  years? 

6.  A  commission  house  spends  $30  a  day  for 
telegrams ;  how  much  is  spent  in  65  days  ? 

7.  If  12  men  earn  $72  in  one  week,  how  much 
will  18  men  earn  in  the  same  time  ? 


50  ft. 


8.  How  many  square  feet  of 
surface  has  the  floor  of  this  room  ? 

How  many  square  yards  of  oil- 
cloth will  be  required  to  cover  the 
floor? 


18.    Find  quotients : 

48  )  24396  (  508  The  divisor  is  not  contained  in 

240  the   second    partial    dividend    (39 

396  tens) ;  write  0  in  tens'  place,  and 

384  annex  6  units  to   form   a   partial 

"l2  remainder,  dividend. 

32019 -f- 53  22592 -f- 32  14687 -f- 48  14689-7-36 
11043  -f-  27  40417 -r- 57  19469 -r- 64  25424 -f- 28 
37482  -f-  93      38577  -f-  77      63150-^-89      27124 -r- 54 


212  ELEMENTARY  ARITHMETIC. 

19.  1.  A  man,  having  $18432,  deposited  $558, 
and  with  the  remainder  bought  land  at  $54  an 
acre ;  how  many  acres  did  he  buy  ? 

2.  A  buys  83  horses  for  $12035,  and  B  buys 
97  acres  of  land  for  $18915;  what  is  the  differ- 
ence in  value  between  one  of  A's  horses  and  one 
of  B's  acres  of  land  ? 

3.  What  will  it  cost  to  pave  a  street  1  mile 
(5280  feet)  long  and  60  feet  wide,  at  37  cents  a 
square  foot? 

4.  Find  the  cost  of  a  piece  of  oilcloth  24  feet  long 
and  15  feet  9  inches  wide,  at  85  cents  a  square  yard. 

5.  A  train  leaves  a  certain  station  at  4  a.  m., 
running  at  the  rate  of  28  miles  an  hour;  a  second 
train  leaves  the  same  station  two  hours  later,  run- 
ning in  the  same  direction  at  the  rate  of  36  miles 
an  hour.  When  will  the  fast  train  overtake  the 
slow,  and  how  far  from  the  starting  place  ? 

Hint.  Gain  in  1  hour,  8  miles.  56  miles  to  he  gained.  56  miles  -r  8 
miles  =  7.     How  far  has  the  fast  train  travelled  in  7  hours  1 

6.  If  the  remainder  is  17,  the  quotient  75,  and 
the  dividend  45767,  what  is  the  divisor? 

20.     ORAL    REVIEW. 

1.  If  40  men  can  do  a  piece  of  work  in  10  days, 
in  what  time  could  8  men  do  the  same  work  ? 

2.  In  my  farm  are  120  acres ;  ^  of  it  is  in 
meadow,  ^  in  wheat,  and  the  rest  in  woodland. 
What  part  is  wroodland  ?      How  many  acres  ? 


REVIEW.  213 

3.  A  stationer  bought  12  dozen  pens  at  5  cents 
a  dozen,  and  sold  them  two  for  a  cent ;  what  did 
he  gain? 

4.  I  had  $120.  I  spent  J  of  it  for  a  watch,  \ 
of  it  for  an  overcoat,  and  ^  of  it  for  board ;  how 
much  had  I  left  ? 

5.  A  man  had  a  dozen  boxes  of  candy,  each  box 
containing  10  pounds.  If  he  makes  of  it  packages 
containing  one  half-pound  each,  how  many  pack- 
ages will  he  have  ? 

6.  A  man  carried  4|  pecks  of  cherries  to  market, 
and  sold  them  at  ten  cents  a  quart ;  how  much  did 
he  receive  for  them  ? 

7.  At  2  cents  a  square  foot,  what  will  \2\ 
square  yards  of  wire  cloth  cost? 

8.  Find  the  cost  of  10  yards  of  calico  at  14  cents 
a  yard,  and  8  yards  of  ribbon  at  20  cents  a  yard  ? 

9.  A  lady  paid  \  of  a  dollar  for  a  thimble,  f  of  a 
dollar  for  braid,  and  &  of  a  dollar  for  thread.  How 
many  hundredths  of  a  dollar  did  each  cost  ?  How 
much  money  did  she  spend? 

10.  James  had  $100,  and  spent  \  of  it  for  a 
watch  and  ft  for  a  coat.  How  much  money  did 
he  have  left  ? 

11.  Give  the  squares  of  all  the  numbers  from 
1  to  10. 


214  ELEMENTARY  ARITHMETIC. 

21.  Find  products: 

8094  x  208  =  ?  8094  x  100  =  ? 

8094    8094 

208    100 

8  times  8094=  64752  8094  (hundreds)  =  809400  units. 
200  "  8094  =  16188 
208  "  8094  =  1683552 

Note.  When  the  multiplier  is  10,  100,  1000,  etc.,  the  product  is  ob- 
tained by  annexing  as  many  zeros  to  the  multiplicand  as  there  are  zeroa 
in  the  multiplier.     8094  X  100  =  809400. 

1.  2965  x  284  7.  3098  X  769  13.  3548  x  368 

2.  3472  x  409  8.  4837  X  694  14.  6497  x  309 

3.  5409  x  538  9.  6789  x  358  15.  3859  x  276 

4.  5696  x  607  10.  2864  x  708  16.  9294  x  509 

5.  2897  X  986  11.  2022  x  100  17.  6789  x  698 

6.  3587  X  659  12.  4967  x  967  18.  3008  X  987 


22.  PROBLEMS. 

1.  A  stationer  buys  4  gross  lead  pencils  at 
$3.75  a  gross,  and  retails  them  at  8  cents  each; 
how  much  does  he  gain  ? 

2.  The  Civil  War  began  in  1861 ;  how  long 
ago  was  that? 

3.  What  will  be  the  cost  of  slating  a  roof,  38 
feet  long  and  27  feet  wide,  at  $3.50  a  square 
yard? 

4.  A  fruit  dealer  bought  6  bushels  of  peaches 
at  $3.50  a  bushel,  and  sold  them  at  15  cents  a 
quart ;    did  he  gain  or  lose,  and  how  much  ? 


PROBLEMS. 


215 


5.  What  is  the  cost  of  a  cable  972  feet  long,  at 
95  cents  a  yard  ? 

6.  A  farmer  has  8  ten-acre  lots,  in  each  of  which 
he  pastures  8  cows;  each  cow  produces  114  pounds 
of  butter,  for  which  he  receives  16^  cents  a  pound; 
the  expenses  for  each  cow  are  $5.50.  How  much 
does  he  make  by  his  dairy  ? 

7.  Bought  6  reams  of  foolscap  paper  at  $2.75  a 
ream ;  sold  \  of  it  at  25  cents  a  quire,  and  the  re- 
mainder at  the  rate  of  4  sheets  for  6  cents.  How 
much  did  I  make  ? 


23.    Find  quotients: 


1.  133215-7-107 

2.  347655 -f- 215 

3.  809437  -f-  621 

4.  217892 -f- 493 

5.  1130493 -v- 533 


7.  444280 -T- 232 

8.  519013-f-319 

9.  923257-f-862 

10.  707861-f-639 

11.  753538 -T- 671 


13.  766080-7-315 

14.  660303  -r-  423 

15.  735289-f-599 

16.  603972 -T- 224 

17.  487228-f-827 


6.     653219  4-394      12.   219763-^-995      18.   701101-7-901 


24.      PROBLEMS. 

1.  The  President  of  the  United  States  receives 
$50000  a  year;  how  much  is  that  a  day  ? 

2.  Fairview  Park  consists  of  480  acres,  for 
which  $180000  was  paid;  how  much  was  that 
per  acre  ? 

3.  If  46  acres  of  land  produce  2484  bushels  of 
corn,  how  many  bushels  will  120  acres  produce  ? 


216  ELEMENTARY  ARITHMETIC. 

4.  There  are  30000  voters  in  our  city ;  count- 
ing this  as  one  fourth  of  the  population,  how 
many  people  have  we?  There  a're  150  precincts; 
that  gives  an  average  of  how  many  votes  for 
each  precinct? 

5.  A  farmer  sold  26  dozen  eggs  at  22|  cents  a 
dozen,  and  16  pounds  of  butter  at  28£  cents  a 
pound.  He  received  in  payment  2  pounds  of  tea 
at  65  cents  per  pound,  3  yards  of  cloth  at  $2.50 
per  yard,  and  the  remainder  in  money.  How 
much  money  did  he  receive  ? 

6.  Lafayette  was  born  in  1757,  and  entered  the 
American  army  in  1777;  how  old  was  he  at  that 
time? 

7.  The  total  population  of  North  America  in  1890 
was  80280990;  that  of  Europe  was  339668156. 
What  was  the  difference  in  population  ? 

8.  Mt.  Cenis  tunnel  is  7i>  miles  long  ;  how  many 
feet  is  that  ? 

9.  Could  a  vessel  sail  f  of  the  way  round  the 
globe  in  a  direct  line  ?  If  it  could,  how  many 
miles  would  it  sail? 

10.  How  many  cubic  inches  in  a  block  of  ice, 
which  is  2  feet  long,  2  feet  wide,  and  1  foot  thick  ? 

11.  The  population  of  Chicago  in  1880  was 
503189;  in  1890  it  was  1099850.  Find  the 
increase  for  ten  years. 


PROBLEMS.  217 

12.  A  milkman  paid  a  farmer  $3.20  for  10  two- 
gallon  cans  of  milk.  He  lost  5  gallons.  At  what 
price  per  quart  must  he  sell  the  remainder  to  gain 
8  cents  per  gallon  on  the  whole  amount  purchased  ? 

Hint.  20  gallons  at  8  cents  =  $1.60  to  be  gained.  $3.20  -|-  $1.60  = 
selling  price  of  15  gallons. 

13.  In  Elgin,  111.,  an  average  of  1200  watches 
are  made  each  week-day.  At  that  rate,  how  many 
watches  are  made  there  in  a  year,  allowing  five 
holidays  ? 

14.  If  60000000  bushels  of  wheat  are  har- 
vested in  Indiana  this  year,  what  wTill  it  be  worth 

.  at  an  average  of  78  cents  per  bushel  ? 

15.  If  8  pounds  of  wool  are  obtained  from  one 
sheep  in  one  year,  how  many  pounds  at  that  rate 
will  48  sheep  yield  in  3  years  ?  What  will  it  be 
worth  at  30  cents  a  pound  ? 

16.  3000  cocoons  make  only  about  a  pound  of 
raw  silk.  To  make  2  ounces  would  require  how 
many  cocoons  ? 

17.  Our  lot  fronts  221  feet  of  Chestnut  Street, 
and  123  feet  of  Hill  Street ;  how  many  yards  of 
outside  fence  have  we  ? 

Our  sidewalk  is  5  feet  wide ;  how  many  square 
yards  of  pavement  have  we  ? 

18.  The  first  locomotive  was  used  in  our  country 
in  1829.     How  long  ago  was  that  ? 


218 


ELEMENTARY  ARITHMETIC. 


25.    Find  quotients : 


1.  774648 -M86  = 

1    9.  614307 -f  199=?   17. 

17820^294  =  ? 

2.  295470  -M90  = 

I    10.  4722354 -M78  =  ' 

18. 

632008  -f-  196  =  1 

3.  937387 -f  184  = 

*    11.  2966607 -f-  189  = 

1   19. 

657320 -^  178  =  ? 

4.  7210473 -M  87  = 

!    12.  713513 -r  179  =  ' 

1        20. 

845679 -M 68  =  ? 

5.  8043840 -r  194=' 

»    13.  2154003-^399  = 

i        21. 

2474420^307  =? 

6.  842877  — 179  = 

14.  1604083 -r  987  =  ' 

22. 

15604064^-196  =  ? 

7.  145260-^-108  =  ' 

!    15.  685176 -M97  =  ' 

23. 

583700  -f  395  =  ? 

8.  1874774 -f-172=' 

16.  1 260524 -M  59  =  ' 

24. 

3500872  -f  498  =  ? 

26.     ORAL    REVIEW. 

1.  Bought  a  gross  of  penholders  for  80  cents, 
and  sold  them  at  a  cent  apiece;  how  much  was 
made? 

2.  How  many  square  feet  in  a  room  12  feet  by 
15  feet  ?     (Drawing.) 

3.  At  2  cents  a  sheet,  what  will  be  the  cost  of 
5  quires  of  paper  ? 

4.  If  you  are  just  twelve  years  old,  how  many 

months  is  that  ?     How  many  weeks  ? 

5.  How  many  score  in  10  dozen  ? 

6.  A  man  has  a  farm  of  96  acres ;  &  is  in  one 
field,  yi  is  in  another  field,  and  the  rest  is  in 
meadow.  What  part  is  in  meadow  ?  How  much 
is  in  meadow  ?  How  many  acres  in  the  two 
fields  ? 

7.  At  18  cents  a  square  foot,  what  will  be  the 
cost  of  a  piece  of  land  40  feet  long  and  20  feet 
wide? 


REVIEW.  219 

8.  If  11  cents  is  -J-  of  the  cost  of  a  basket,  what 
will  2  baskets  cost  ? 

9.  If  8  apples  cost  11  cents,  how  many  apples 
can  I  get  for  $1.10. 

10.  How  many  square  feet  in  a  brick  sidewalk 
100  feet  long  and  6  feet  wide  ?  What  will  it  cost 
to  make  such  a  walk  at  50  cents  a  square  yard  ? 

11.  A  room  is  11  feet  long  and  18  feet  wide. 
What  is  the  area  of  its  floor  ?  How  many  square 
yards  of  carpet  would  it  take  to  cover  it  ? 

12.  What  will  be  the  cost  of  a  pavement  40  feet 
long  and  9  feet  wide  at  30  cents  a  square  yard  ? 

13.  What  will  be  the  cost  of  natural  gas  for  8 
months  on  one  cook-stove  at  $1  a  month,  two 
grates  at  $1.25  each  per  month,  and  one  base- 
burner  at  90  cents  per  month? 

14.  If  22  men  can  clear  an  acre  of  ground  in  6 
days,  in  how  many  days  can  12  men  clear  it  ? 

15.  If  a  boy  earns  $12  a  month,  how  much 
will  he  earn  in  a  year  ?  If  he  spends  ^  of  it  for 
clothes  and  board,  how  much  will  he  have  left  ? 

16.  Bought  10  bushels  of  peaches  at  $1  a  bushel, 
and  sold  them  at  30  cents  a  peck ;  how  much  was 
gained  ? 

17.  How  many  quarts  of  berries  at  12  cents  a 
quart  will  it  take  to  pay  for  8  yards  of  cloth  at 
16^  cents  a  yard? 


Dining  Hall. 


220  ELEMENTARY  ARITHMETIC. 

18.  Our  room  is  30  feet  square.  How  much 
would  picture  molding  for  it  cost  at  2  cents  per 
foot  ?  How  many  square  feet  of  ceiling  have  we  ? 
How  many  square  feet  of  surface  has  the  floor  ? 

27.      PROBLEMS. 

^^ ,         1.    What  will  it  cost  to  cover  this 

hall  with  oilcloth,  one  yard  wide,  at 
40  cents  a  yard  ? 

2.  The  ceiling  is  12  feet  high  ;  how 
many  square  feet  in  the  four  walls? 
What  will  it  cost  to  paint  the  walls  at  57  cents 
per  square  yard  ? 

3.  A  town  lot  containing  4800  square  feet  is  40 
feet  wide  on  the  street.  How  deep  is  it  ?    (Drawing.) 

4.  If  a  schoolboy  is  8  minutes  late  every  day, 
how  much  time  does  he  lose  in  115  days  ? 

5.  St.  Gothard  tunnel  is  9  miles  long;  how 
many  feet  long  is  it  ? 

6.  Abraham  Lincoln  was  born  in  1809.  Be- 
tween the  ages  of  7  and  21  he  lived  in  southern 
Indiana ;   between  what  dates  did  he  live  there  ? 

7.  The  number  of  bales  of  cotton  produced  in 
the  United  States  in  1890  was  6940898,  of  which 
Texas  produced  1594305  bales;  how  many  bales 
were  produced  by  the  other  Southern  States? 


MISCELLANEOUS  PROBLEMS. 


221 


28.    Find  quotients : 


1. 

246573  4 

-  1212 

9. 

863973  - 

;-  2652 

17. 

631253 

4-  3251 

2. 

7452014 

-  2373 

10. 

915761  - 

^  2483 

18. 

2187923 

4-2473 

3. 

1793257  -r 

-  6253 

11. 

3621487  - 

'-  7193 

19. 

4267942 

4-8198 

4. 

4175959  -5- 

7329 

12. 

8724165  - 

~  3998 

20. 

4250963 

4-  9876 

5. 

9180257  4- 

6351 

13. 

2153897  - 

r  8253 

21. 

7953621 

4-  9957 

6. 

7221483  4 

■  992 

14. 

11853221  - 

~  8123 

22. 

2170821 

4-  6125 

7. 

1250921  4- 

9253 

15. 

5995871  - 

•r  6751 

23. 

84371285 

-h  695 

8. 

27263579 -^ 

1371 

16. 

42507633  -■ 

-8952 

24. 

97239643 

+  9853 

29.      MISCELLANEOUS    PROBLEMS. 

1.  Rhode  Island  contains  1085  square  miles, 
Montana  145310  square  miles  ;  how  many  States 
as  large  as  Rhode  Island  could  be  made  out  of 
Montana,  and  how  many  square  miles  will  be 
left  over  ? 

2.  A  miller  purchased  2149  bushels  of  wheat, 
weighing  128940  pounds.  What  was  the  weight 
of  1  bushel? 

3.  A  road  was  constructed  at  a  cost  of  $4328 
per  mile,  and  the  total  cost  was  $8331400;  how 
many  miles  long  is  the  road  ? 

4.  In  1890  South  Dakota  raised  21152000  bush- 
els of  wheat.  How  many  bushels  would  that  be 
for  each  of  the  2251  people  in  Bismarck,  and  how 
many  bushels  over  ? 

5.  In  one  cubic  foot  there  are  1728  cubic  inches. 
How  many  cubic  feet  are  there  in  a  pile  of  wood 
containing  13939776  cubic  inches? 


222 


ELEMENTARY  ARITHMETIC. 


Parlor. 

16  x  18. 


6.  In  1890  the  mining  products  of  the  United 
States  were  estimated  at  $256258276,  and  the 
manufacturing  products  $6443495029 ;  what  was 
the  difference  in  their  value  ? 

7.  If  a  certain  State  has  2324  public  schools,  and 
the  apportionment  of  school  money  is  $7030100, 
what  would  be  the  average  cost  per  school  ? 

8.  How  many  church  bells,  weighing  3421  lbs. 
each,  can  be  made  from  2753905  lbs.  of  bell  metal  ? 

9.  (a)  How  many  square  feet  in  each  of  the 

rooms  on  the  ground 
floor  of  this  house  ? 

(6)  How  much  will 
it  cost  to  cover  these 
floors  with  yard-wide 
material  at  the  fol- 
lowing prices :  Parlor 
carpet  at  $1.25  per 
yard  ;  sitting  and  bed- 
room matting  at  65 
cents  per  yard ;  din- 
ing room  and  kitchen 
oilcloth  at  95  cents 
per  yard  ? 

(c)  What  will  it 
cost  for  picture  mold- 
ing for  all  the  rooms,  except  the  kitchen,  at  12 
cents  a  yard? 


Bed-Room. 
13  x  15. 


Sitting-Room. 
14  x  18. 


Kitchen 
14  x  15. 


DINING-ROOM. 

12  x  15. 


MISCELLANEOUS  PROBLEMS.  223 

10.  What  time  elapsed  from  the  battle  of  Lex- 
ington, 1775,  to  the  firing  upon  Fort  Sumter, 
1861? 

11.  If  I  buy  real  estate  for  $854657,  agreeing 
to  pay  for  it  in  yearly  payments  of  $37159  each, 
how  many  payments  will  I  make  ? 

12.  The  improved  land  of  the  United  States  is 
estimated  at  207198720  acres;  how  many  town- 
ships of  23040  acres  each  could  be  made  from 
this  land  ? 

13.  In  a  pile  of  4701625  bricks  how  many  loads 
are  there,  if  each  load  contains  1000  bricks  ? 

14.  Charlie  saw  a  box  car  marked  "  Weight 
28000  pounds."  A  ton  is  2000  pounds.  What  is 
the  weight  of  the  car  in, tons  ? 

15.  What  will  be  the  cost  of  whitening  the  ceil- 
ing and  walls  of  a  schoolroom  44  feet  long,  28  feet 
wide,  and  13  feet  high,  at  5  cents  a  square  yard,  if 
20  square  yards  are  deducted  for  doors,  windows, 
and  baseboards? 

16.  Find  the  sum  of  sixteen  million  one  thou- 
sand twenty,  twelve  million  one  hundred  twenty- 
eight,  nine  million  thirteen  thousand  two,  seven 
million  sixteen  thousand  seven,  and  three  hundred 
million  nine. 


224  ELEMENTARY  ARITHMETIC. 

17.  How  many  years  from  the  Centennial  ex- 
hibit at  Philadelphia  in  1876  to  the  Columbian 
exhibit  at  Chicago  in  1893? 

18.  In  a  field  of  turnips  there  are  296  rows,  and 
each  row  yields  18  bushels.  How  many  loads  of 
30  bushels  each  in  the  field  ? 

19.  $557283  added  to  a  certain  number  of  dol- 
lars will  produce  $1157003  ;  what  is  the  number  ? 

20.  If  68  pounds  of  coal  are  consumed  in  carry- 
ing a  train  one  mile,  how  many  pounds  will  be 
consumed  at  that  rate  in  going  1894  miles  ? 

21.  What  is  the  weight  of  a  train  of  six  cars  if 
the  baggage  car  weighs  6000  pounds,  the  express 
car  58000  pounds,  the  sleeping  car  80000  pounds, 
and  each  of  three  passenger  cars  54000  pounds? 
How  many  tons  is  that  ? 

30.     DIVISORS    AND    MULTIPLES. 

What  integer  greater  than  1  will  exactly  divide 
12,  20,  and  24  ?  4  will  divide  each  of  these  num- 
bers, and  is  called  a  common  divisor;  it  is  a  divi- 
sor common  to  all  of  them.  What  number  greater 
than  1  will  exactly  divide  25,  30,  and  35  ? 

31.  A  Common  Divisor  of  two  or  more  numbers 
is  any  whole  number  greater  than  1,  which  will 
exactly  divide  each  of  them. 


DIVISORS  AND  MULTIPLES.  225 

Find  the  greatest  number  which  will  exactly 
divide  18,  27,  and  36.  9  is  the  greatest  common 
divisor  of  these  numbers. 

What  is  the  greatest  common  divisor  of  30,  45, 
60,  and  90  ? 

32.  The  Greatest  Common  Divisor  of  two  or 
more  numbers  is  the  greatest  exact  divisor  of 
each  of  them. 

The  product  of  all  the  prime  factors  common 
to  two  or  more  numbers  is  their  Greatest  Common 
Divisor  (G.  C.  D.). 

33.  Find  the  greatest  common  divisor  of  70 
and  180. 

Separate  the  numbers  into  their  prime  factors.      The 

prime  factors  common  to  70  and 
70  =  2  x  7  X  5.  18Q  are  2  and  5>     1Q  ig  the  pro_ 

r  180  =  2x9x5x2     duct  Qf  2  and  ^  and  ig  the  grmt_ 
2  X  5  =  10,  G.  C.  D.         est  common  divisor  of  70  and  180. 

Find  the  greatest  common  divisor  of : 

1.  84  and  90  8.  64  and  114  15.  216  and  360 

2.  36  and  78  9.  56  and  126  16.  182  and  196 

3.  36  and  90  10.  39  and  273  17.  42,  133,  and  56 

4.  65  and  91  11.  120  and  132  18.  32,  48,  and  128 

5.  48  and  128  12.  125  and  175  19.  56,  63,  and  315 

6.  24  and  105  13.  150  and  275  20.  96,  48,  60,  and  108 

7.  63  and  108  14.  126  and  264  21.  75,  225,  and  500 

15E 


226  ELEMENTARY  ARITHMETIC. 

34.     MULTIPLES. 

Name  a  number  that  is  3  times  9.  27  is  a  Mul- 
tiple of  9 ;  it  is  also  a  multiple  of  3.  A  multiple 
of  3  is  the  product  of  3  multiplied  by  any  whole 
number.  A  multiple  of  9  is  any  number  of 
times  9.  24,  21,  and  28  are  multiples  of  what 
numbers  ? 

35.  A  Multiple  of  a  Number  is  any  integral  (or 
whole)  number  of  times  that  number. 

Find  the  multiples  which  3  and  5  have  in  com- 
mon. Of  the  common  multiples  15,  30,  45,  and 
60,  which  is  the  least  ? 

36.  A  multiple  that  is  common  to  two  or  more 
numbers  is  called  a  Common  Multiple,  and  the  least 
of  the  common  multiples  is  called  the  Least  Com- 
mon Multiple  (L.  C.  M.). 

37.  Find  the  L.  C.  M.  of  27,  24,  and  30. 

27  =  3  x  3  x  3 
24  =  3x2x2x2 
30  =  3x2x5 
2x2x2x3x3x3x5  =  1080,  L.  C.  M. 
Eesolve  27,  24,  and  30  into  their  prime  factors.     Select 
the  different  factors  and  repeat  each  as  many  times  as  it  is 
found  in  any  one  of  the  numbers.     The  product  of  2,  2,  2, 
3,  3,  3,  and  5  is  the  L.  C.  M.  of  27,  24,  and  30. 

A  multiple  of  a  number  must  contain  at  least  all  the 
prime  factors  of  that  number. 

The  least  common  multiple  of  two  or  more  numbers 
must  contain  all  the  prime  factors  that  enter  into  each 
of  them,  and  no  others. 


CA  N  CELL  A  TION.  227 

Find  the  L.  C.  M.  of : 

1.  42,  48,  and  54  8.  44,  88,  and  108  15.  148,  164,  and  248 

2.  14,  24,  and  36  9.  30,  45,  and  60  16.  548,  624,  and  680 

3.  26/32,  and  36  10.  17,  51,  and  119  17.  308,  416,  and  456 

4.  12,  18,  and  96  11.  21,  43,  and  63  18.  432,  528,  and  564 

5.  24,  63,  and  84  12.  120,  180,  and  240  19.  28,  72,  84,  and  96 

6.  27,  33,  and  54  13.  236,  284,  and  320  20.  32,  48,  60,  and  72 

7.  20,  36,  and  54  14.  482,  520,  and  564  21.  32,  36,  49,  and  56 

38.     CANCELLATION. 

Find  the  quotient  of  4  x  6  divided  by  2  x  6. 
Of  4  x  8  divided  by  2  x  8. 

(4X7)^.(2x7)  =  ?         (6x8)-r(3xS)  =  ? 

2  times  any  number  is  contained  in  4  times 
that  number,  how  many  times  ? 

(6x7)v(3x7)=?  (9x5)^(3x5)  =  ? 

3  x  9  is  contained  in  6  x  9  as  many  times  as  3 
is  contained  in  what  ?  3  times  any  number  is  con- 
tained how  many  times  in  6  times  that  number  ? 

39.  To  find  quotients  by  the  shortest  method, 
strike  o\it  equal  factors  from  the  dividend  and 
the  divisor. 

Divide  : 

9x7  by  3x7        8x9  by  4x9        8  x  11  by  2  x  11 
12  xo  by  6x5         9x6  by  3x6         9x9  by  3x9 

Dividing  both  dividend  and  divisor  by  the  same 
number  does  not  affect  the  quotient. 

The  process  of  striking  out  equal  factors  from 
the  dividend  and  the  divisor  is  called  Cancellation. 


228  ELEMENTARY  ARITHMETIC. 

40.   Divide  18  x  5  x  6  by  7  x  4  x  5. 

Cancel  the  common  factor  5  from  both  dividend  and  divi- 
sor, and  the  common  factor  2  from 
jo      s      a      07  ®  *u  t^ie  dividend  and  4  in  the  divi- 

~- — ~ — —  =  -=-  =  3f     sor.     Cancel  the  remaining  factor  2 
2  from  the  4  in  the  divisor  with  the 

factor  2  in  18  in  the  dividend.  The 
product  of  the  factors  remaining  in  the  dividend  is  27,  and 
of  those  in  the  divisor,  7.  27  divided  by  7  gives  the  quo- 
tient 3f 

Divide  9x2x6  by  6x6x3. 

Note.  When  the  divisor  equals  the  dividend,  the  quotient  is  1. 
This  result  will  be  found  when  all  the  factors  of  the  dividend  and  the 
divisor  are  canceled. 

27  X  6  x  2  x  7 


18 

X  6 

X9 

10 

X  7 

X6 

14 

X  7 

X5 

15 

X  6 

X  2 

16 

X9 

X21 

18  X  3  x  4 

X2 

25  x  0  x  6 

X5 

18  x  6  x  4 

X3 

18  x  22  x 

28 

75 

X 

9  x  06 

12 

X 

15 

X  9 

87 

X 

15 

X9 

5 

X 

9  x 

:  29 

51 

X 

54 

Xl2 

15  x  12  x  4  21  x  33  x  7  36  X  17  x  3 

41.     PROBLEMS. 

1.  How  many  pounds  of  sugar  at  6  cents  a 
pound  can  be  bought  for  9  yards  of  calico  at  12 
-cents  a  yard? 

9  x  12  cents  equals  the  cost  of  the 
*    w  =  18    calico.      As    many   pounds    of    sugar 
must  be  given  for  the  calico  as  there 
are  6  cents  in  9  x  12  cents. 


PROBLEMS.  229 

2.  How  many  pairs  of  shoes  at  $3.00  a  pair 
must  be  given  in  exchange  for  30  bushels  of 
potatoes  at  50  cents  a  bushel  ? 

3.  A  farmer  sold  to  a  grocer  19  bushels  of  apples 
at  75  cents  a  bushel,  and  took  his  pay  in  coffee 
at  30  cents  a  pound:  How  many  pounds  did  he 
receive  ? 

4.  A  milkman  sells  daily  50  quarts  of  milk  at  6 
cents  a  quart.  How  many  yards  of  carpet  at  90 
cents  a  yard  can  be  bought  for  the  milk  sold  in 
7  days  ? 

5.  For  12  days'  work  of  8  hours  each  a  work- 
man received  $24.  How  much  at  that  rate  would 
he  receive  for  18  days'  work  of  9  hours  each  ? 

6.  Mr.  Jones  sold  121  pounds  of  beef  at  14 
cents  a  pound,  and  took  his  pay  in  potatoes  at 
77  cents  a  bushel ;  how  many  bushels  did  he 
receive  ? 

7.  On  each  of  6  days  a  grocer  sold  150  pounds 
of  sugar  at  8  cents  a  pound.  How  many  pounds 
of  tea  must  he  sell  on  each  of  4  days  at  60  cents 
a  pound  to  equal  the  amount  he  received  for  the 
sugar  ? 

8.  Make  a  problem  for  24  divided  by  3  x  2. 

9.  Make  a  problem  for  45  divided  by  3x5. 


CHAPTER  IV. 


COMMON    FRACTIONS. 

1.  A  Fraction  is  one  or  more  of  the  equal 
parts  of  a  unit. 

One  of  the  equal  parts  into  which  the  unit  is  divided 
is  a  fractional  unit.  The  value  of  a  fraction  depends  both 
'upon  the  size  of  the  fractional  unit  and  the  number  of  frac- 
tional units  expressed. 

How  many  halves   in  a  dollar  ?   an  apple  ?   a 

bushel  ?    a    mile  ?      How    many    thirds    in    an 

orange  ?   a  loaf  of  bread  ?     How  many  sevenths 

in  a  peck  ?   in  a'  quart  ? 

2.  A  fraction  is  expressed  by  two  numbers, 
one  written  under  the  other,  with  a  horizontal 
line  between  them  ;    as,  |,  %  1,  etc. 

The  number  below  the  line  shows  the  number 
of  equal  parts  into  which  the  unit  is  divided ; 
it  is  called  the  Denominator. 


COMMON  FRACTIONS.  231 

The  number  above  the  line  shows  the  number 
of  equal  parts  taken  in  the  fractional  number ;. 
it  is  called  the  Numerator. «  The  numerator  and 
denominator  are  called  the  Terms  of  a  fraction. 

3.  Read  the  following  fractions.  In  each  case 
tell  into  how  many  parts  the  unit  is  divided. 

I       A      A       i       A      A      A      A      if 

i?      «      if      «      «      M      ii      II      if 

m    st    i#    n    a    n    u    u    n. 

Express  the  following  in  figures  : 

Six  ninths.  Seven  thirty-fourths. 

Seven  elevenths.  Twelve  twenty -eighths. 

Nine  twelfths.  Sixteen  fiftieths. 

Ten  fourteenths.  Fourteen  fortieths. 

Six  thirteenths.  Twenty  forty-ninths. 

Seven  twenty-fifths.  Nineteen  forty-fifths. 

Eight  nineteenths.  Twenty-nine  sixtieths. 
Nine  thirtieths. 

4.  A  Proper  Fraction  is  one  whose  value  is 
less  than  one ;  as,  §,  f,  J.  The  numerator  of  a 
proper  fraction  is  less  than  the  denominator. 

5.  An  Improper  Fraction  is  one  whose  value 
is  equal  to,  or  greater  than,  one  ;  as,  f,  I,  |.  The 
numerator  is  equal  to,  or  greater  than,  the  de- 
nominator. 

6.  A  Mixed  Number  is  an  integer  and  a  frac- 
tion united ;   as,  3J,  4|,  29|. 


232  ELEMENTARY  ARITHMETIC. 

7.  To  reduce  integers  and  mixed  numbers  to  fractions. 
How  many  fourths  in  an  orange  ?     How  many 

fourths  in   6   oranges?      How  many  fifths   in    a 

melon  ?     In  3  melons  ? 

In  one  melon  there  are  five  fifths ;  in  3  melons  there  are 
three  times  five  fifths. 

How  many  sevenths  in  4  ?     In  6  ?     In  8  ? 

How  many  thirds  in  31  loaves  of  bread  ? 

In  one  loaf  there  are  three  thirds.  In  three  loaves  there 
are  nine  thirds.  Nine  thirds  and  one  third  are  ten  thirds. 
There  are  ten  thirds  in  3J  loaves  of  bread. 

How  many  sixths  in  41  ?     3£?     5J ? 

How  many  sevenths  in  4^  ?     6?  ?     8f  ? 

How  many  tenths  in  3&  ?     6i|  ?     5&  ? 

How  many  ninths  in  14  apples  ? 

1  apple  =  f . 
14  apples  =  14  times  g  =  J-g&.     Ans. 

Reduce  to  improper  fractions: 

1.  25^-    4.  94^    7.  136|    10.  98^    13.  67^  16.  143^ 

2.36&    5.  86 A    8.  342 J    11.  87 A    *4.  92T%  17.  294  ^ 

3.  45A    6.92ft    9.425f    12.  75&    15.  78Tfo  18.  673Tftfo 

8.  Reduce  14g  to  ninths. 

1  =  |.     14  =  14  times  f  =  if*,     if*  +  J  =  if*.  Ans. 

Reduce : 

1.  182  to  thirds.     3.  284  to  fifths.  5.  53§  to  ninths. 

2.  25J  to  sixths.    4.  49?  to  sevenths.     6.  64^  to  twelfths. 

Write  a  rule  for  reducing  a  mixed  number  to  a 
fraction. T 


COMMON  FRACTIONS.  233 

9.    T©  reduce  fractions  to  integers  or  mixed  numbers. 

How  many  yards  in  six  half-yards  ?  How 
many  apples  in  nine  half-apples  ?  How  many 
pears  in  11  half -pears  ? 

There  are  two  half-pears  in  one  pear.     In  11  half-pears 
there  are  as  many  pears  as  there  are  2's  in  11. 
2)11 

5£  times.     There  are  5J  pears  in  11  half-pears. 

How  many  gallons  in  26  half-gallons  ?  How 
many  bushels  in  17  half-bushels  ? 

How  many  melons  in  18  thirds  of  a  melon  ? 

How  many  yards  in  18  thirds  of  a  yard  ? 

How  many  ones  in  20  fifths  ?  In  28  fourths  ? 
In  26  sevenths  ?  In  25  eighths  ?  In  35  ninths  ? 
In  86  elevenths  ?  In  96  twelfths  ?  In  89  tenths  ? 
In.f?  In  f  ?  In??  In  g?  In  i?  In  £  ? 
In  V?? 

Write  a  rule  for  changing  an  improper  fraction 
to  an  integer  or  a  mixed  number. 

Reduce  to  an  integer  or  a  mixed  number  : 

i-W  s-H*  5-W  7-W-    *W  "-W  13-W    i*-1*** 

2-W  4--W  6-W  8.^  io.  w  12. -w  14.4^  16--¥(n?- 

XO.    To  reduce  fractions  to  lowest  terms. 

One  fifth  of  a  dollar  is  how  many  cents  ?  Two 
tenths  of  a  dollar  ?     |  is  how  many  tenths  ? 

I  of  a  yard  is  how  many  inches  ?  J  is  how  many 
sixths  ? 


234  ELEMENTARY  ARITHMETIC. 

t  are  how  many  thirds  ? 

How  many  fourths  in  |  of  an  apple  ? 

Note.  If  necessary,  these  equivalent  fractions  should  be  illustrated 
by  folding  strips  of  paper  or  paper  discs. 

&  are  equal  to  how  many  fifths  ? 

Change  the  form  of  the  fraction,  not  the  value, 
by  increasing  the  size,  and  reducing  the  number  of 
parts  into  which  the  unit  is  divided. 

I  =  £.  6  tenths  are  equal  to  as  many  fifths  as 
there  are  &  in  $•  &  in  &  three  times.  There  are 
three  fifths  in  &. 

The  form  of  the  fraction  may  be  changed  with- 
out changing  its  value,  by  dividing  both  terms  by 

the  same  number. 

6-4-2  =  3 

10  -f-  2  =  5 

Reduce  &  and  ft,  each  to  fourths. 
Reduce  §,  |1?  and  i,  each  to  sevenths. 
Reduce  %  i,  |f,  and  %  each  to  eighths. 
Reduce  §j,  2|,  i,  and  ^,  each  to  ninths. 
When  a  fraction  is  reduced  to  an  equivalent  frac- 
tion, with  smaller  terms,  it  is  reduced  to  lower  terms. 

11.  A  fraction  is  in  its  loivest  terms  when  no 
integer,  except  1,  will  exactly  divide  both  nu- 
merator and  denominator. 

Reduce  %  to  lowest  terms. 

64^-8       8  8-7-4      2 


96  -r-  8      12        12  -f-  4 


Arts. 


COMMON  FRACTIONS.  235 

The  same  result  will  be  obtained  by  dividing 
both  terms  by  32,  the  greatest  number  which  will 
exactly  divide  both  terms. 

Reduce  to  lowest  terms : 
*-U   3-tVt    5-t¥t    ?•■&%     9.  A2e    11.  to    is-HK    15.  Ht 

2-tf     4-i¥t     <WA     8.^6      10-1%     12-  iff     14.  Hi     16.Jfr 

Make  a  rule  for  changing  a  fraction  to  its 
lowest  terms. 

12.  To  reduce  fractions  to  higher  terms. 

One  fourth  of  an  apple  is  how  many  eighths  ? 

1  are  how  many  eighths  ?     f  ?     J  ?     J?     j  ? 

One  third  is  how  many  ninths  ?     |? 

X  =  |.      |  =  4  times  §  which  are  ^-. 

Change  |  to  eighteenths,  ^  to  twenty-fourths, 
^  to  sixtieths,  ^  to  forty-eighths,  ^  to  seventy- 
seconds. 

When  a  fraction  is  changed  to  an  equivalent  frac- 
tion with  greater  terms,  it  is  reduced  to  higher  terms. 

13.  Change  |,  %  and  1  to  equivalent  fractions 

having  the  same  denominator. 

3  X  6  __  18  5  x  4  _  20  3  X  3_  9 

4~x6  ~~  24  6x4""  24  8  X  3  ~~  24 

When  several  fractions  have  the  same  denomi- 
nator, they  have  a  common  denominator. 

Eeduce  to  equivalent  fractions  with  a  common 
denominator  : 

1.  I,  h  *•        3.   J,  f,  |.        5.   |,  A»  A-        7.   »,  A,  i- 

2.  I,  f ,  i.        4.  fc  ^,  A-      6.  a>  i  A-        8.  |,  «,  a- 


236  ELEMENTARY  ARITHMETIC. 

14.  The  common  denominator  must  be  a  com- 
mon multiple  of  the  denominators  given.  The  least 
common  denominator  must  be  the  1.  c.  m.  of  the 
denominators  given. 

Reduce  to  equivalent  fractions  having  a  least 
common  denominator  : 

1.  h  h  h       3.  J,  j,  j.         5.  f,  ft,  ft.      7.  £,  |,  f 

2.  },  i,  ».        4.   J,  f,  A-        6.   fc  A,  |.        8.   |,  T§T,  JJ. 

15.     ADDITION    OF    FRACTIONS. 

Harry  gave  J  of  a  melon  to  John,  I  to  George, 
and  |  to  Helen  ;  how  many  fifths  of  the  melon 
did  he  give  away  ? 

Jane  gave  \  of  a  dollar  for  some  card-board,  and 
|  of  a  dollar  for  some  needles;  what  part  of  a 
dollar  did  she  spend  ? 

i  =  ft-       t  =  ft-       ft  +  A  =  2V    -<*»»• 

Only  like  fractions  can  be  added. 

To  add  fractions  ;  Change  the  fractions  to  equiva- 
lent fractions  having  a  common  denominator \  «c7d  ffteir 
numerators ,  and  write  the  sum  over  the  common  de- 
nominator. 


Find  the  sum  of 

§  and  f .    4.  §  an 
I  and  £.    5.  J  an 
3.  J  and  f .    6.  I  and  § .    9.  f  and  ft,    12.  ?  and  | 


1.  §  and  f.    4.  §  and  J.    7.  J  and  §.     10.  {  and  ft. 

2.  I  and  £.    5.  J  and  f.    8.  §  and  ft.    U-  I  and  ft. 


SUBTRACTION   OF  FRACTIONS.  237 

16.  Add  M,  and  & 
*  =  A-    t-*tt    A  +  «  +  A  =  f*  =  2A.    ^. 

What  is  the  sum  of  181,  181,  and  U\  ? 
13|       A 

j^x  3  To  add  mixed  numbers : 

14^.  (^  Add  the  fractions  and  the  integers 

4n  .        IT—Ijl     separately,  and  combine  the  results. 

Add  the  following  : 

(1)  I,  I,  A  (*)  h  h  \h  (9)  45i,  67|,  62|. 

(2)  |,  |,  *.  (6)  f,  T7o?  «•  (10)  37i,  18§,  16f. 

(3)  |,  f,  5-  (7)  A,  A  H-  (11)  30J,  66*,  843. 

(4)  |,  5,  ^  (8)  «,  A  A-  (12)  251,  16*,  14*. 

17.     SUBTRACTION    OF   FRACTIONS. 

Frank  had  §  of  an  orange :  he  gave  I  to  George ; 
what  part  of  the  orange  had  he  left  ? 

Helen  had  §  of  a  yard  of  ribbon ;  she  gave  I  a 
yard  to  Mary ;  what  part  of  a  yard  had  she  left  ? 
J  =  |.     £  —  $  =  #  =  £.     She  had  £  of  a  yard  left. 

Minuend  and  Subtrahend  must  be  like  numbers. 

To  subtract  fractions  : 

Change  the  fractions  to  equivalent  fractions  having 
a  common  denominator.  Subtract  the  numerator  of 
the  subtrahend  from  the  numerator  of  the  minuend, 
and  write  the  difference  over  the  common  denomi- 
nator. 


238  ELEMENTARY  ARITHMETIC. 

Subtract : 

1.  f~i  =  ?  6.  f-f=?  11.  ft-t  =  * 

2.  #  —  f  =  ?  7.  J  -  J-  =  ?  12.  f  —  f  =  ? 

3.  *-$  =  ?  8.  A-f  =  ?  13.  A-|  =  ? 
4-  H-#  =  ?  9.  |-*  =  ?  14.  A-?=? 
5.  f-f  =  ?  10.  «-*  =  ?  15.  tt-|-f 

18.  Subtract  18f  from  36f 

5 

301         ii  -s  16  4  cannot  be  taken  from  J.     Take  1 

-jg3  o        from  36,  which  leaves  35. 

17A.  ^.  H-l-» 

Subtract : 

1.  16i-13£  =  ?  4.  23§-8?  =  ?  7.  14*-9§  =  ? 

2.  24J-18J  =  ?  5.  26>  —  16f  =?  8.  33^-25^  =  ? 

3.  10i-8i  =  ?  6.  25g-182  =  ?  9.  66j-45g  =  ? 

19.  1.  A  man  divided  his  property  among  his 
five  children,  giving  \  of  it  to  the  first,  \  to  the 
second,  \  to  the  third,  and  &  to  the  fourth ;  what 
part  did  the  fifth  child  receive  ? 

2.  0  of  my  library  is  History,  ^  Poetry,  |  Sci- 
ence, and  the  remainder  Fiction ;  what  part  is 
Fiction  ? 

3.  If  a  tailor  uses  3f  yards  for  a  coat,  2\  yards 
for  trousers,  and  1  yard  for  a  vest,  how  many 
yards  are  used  in  all  ? 

4.  I  owe  $61.  If  I  pay  |  of  a  dollar,  how  much 
shall  I  then  owe  ? 

5.  If  from  $8i  there  be  taken  $6§,  how  much 
will  remain? 


MULTIPLICATION   OF  FRACTIONS.  239 

20.     MULTIPLICATION    OF    FRACTIONS. 
Fractions  multiplied  by  integers. 

If  a  yard  of  cloth  cost  |  of  a  dollar,  what  will 
3  yards  cost  ? 

3  yards  will  cost  3  times  f  of  a  dollar,  whicli  are  £  of 
a  dollar  =  2\  dollars.  Prove  this  by  finding  3  times  the 
number  of  cents  which  |  of  a  dollar  equal. 

If  Mary  learns  §  of  a  page  of  spelling  in  a  day, 
how  many  pages  will  she. learn  in  4  days  ? 

Multiply : 


1. 

J  by  5. 

4. 

fby9. 

7. 

ft  by  15. 

10. 

6J  by  8. 

2. 

i  by  6. 

5. 

fby7. 

8. 

ft  by  12. 

11. 

7|  by  9. 

3. 

I  by  4. 

6. 

f  by  12. 

9. 

4|  by  6. 

12. 

5*  by  7. 

Note.  Multiply  the  fraction  and  the  integer  separately  and  add  the 
products. 

21.     Integers  multiplied  by  fractions. 

1  time  9  pears  is  9  pears.  Will  \  of  9  pears  be  more 
or  less  than  1  time  9  ?  9  pears  multiplied  by  \  is  \  of  9 
pears,  which  is  3  pears.  9  pears  multiplied  by  §  is  f  of  9 
pears,  which  are  6  pears. 

36  x  |  =  |  of  36.  J  of  36  =  9.  |  of  36  equals  3  times  9, 
which  are  27.     36  X  \  =  27. 

Multiply  : 

1.  24  by  |  4.   18  by  f  7.    84  by  \ 

2.  40  by  %  5.    19  by  J  8.    72  by  § 

3.  36byf  6.    56  by  |  9.    96  by  J 


240  ELEMENTARY  ARITHMETIC. 

22.  Fractions  multiplied  by  fractions. 

How  much  is  1  of  |  of  an  apple  ?  Is  it  more  or 
less  than  1  time  \  ? 

j  X  J  equals  J  of  % .     J  of  $  is  J. 

How  much  is  i  of  |  ?  Is  it  more  or  less  than 
1  time  i? 

3  X  |  equals  J  of  J.     £  of  §  is  y^  ;  f  is  3  times  ^,  which 

What  is  the  cost  of  \  of  a  yard  of  silk,  at  |  of  a 

dollar  a  yard  ?     If  the  silk  were  $1  a  yard,  would 

|  of  a  yard  cost  more  or  less  than  |  of  a  dollar  ? 

One  yard  costs  f  of  a  dollar. 

\  of  a  yard  costs  J  of  f ,  which  is  fa  of  one  dollar. 
|  of  a  yard  costs  3  times  fa,  which  is  J- j  =  J  of  a  dollar. 
Prove  this  by  giving  the  price  of  one  yard  in  cents,  in- 
stead of  in  the  fractional  parts  of  a  dollar. 
Short  Process,     f  X  f  =  £$  =  i-    Ans. 

23.  To  multiply  one  fraction  by  another. 

Multiply  the  numerators  together  for  a  new  nume- 
rator, and  the  denominators  together  for  a  new  de- 
nominator, and  reduce  the  resulting  fraction  to  its 
lowest  terms. 

Note.  Show  how  the  process  may  be  shortened  in  this  case  bv 
cancellation. 


Multiply : 

1.     *  by  f .       6. 

f  by  f . 

11. 

*  by  |. 

16. 

A  by  *. 

2.     |by#.       7. 

ibyf- 

12. 

1  by  |. 

17. 

A  by  J 

3.     *by*.        8. 

f  by  f . 

13. 

i  by  «• 

13. 

A  by  f 

4.   2jbyf.        9. 

61  by  J. 

14. 

6J  by  21. 

19. 

61  by  61 

5.   3J  by  |.      10.   2J  by  2J.      15.   5§  by  3J.      20.   8^  by  8f . 


DIVISION  OF  FRACTIONS.  241 

24.  1.  If  a  man  mows  1  of  an  acre  in  a  day, 
how  much  does  he  mow  in  |  of  a  day  ? 

2.  What  is  the  cost  of  \  of  a  yard  of  flannel,  at 
1  of  a  dollar  a  yard  ? 

3.  If  silk  is  worth  f  of  a  dollar  a  yard,  what  is 
1  of  a  yard  worth  ? 

4.  If  a  knife  is  worth  &  of  a  dollar,  and  a  slate 
|  as  much,  what  is  the  slate  worth  ? 

5.  At  |  of  a  dollar  a  pound,  what  is  ^  of  a  pound 
of  tea  worth  ? 

6.  If  4  yards  of  velvet  cost  $61,  how  much  more 
than  $8  will  12  yards  cost  ? 

7.  The  captain  of  a  merchant  ship  owns  |  of  the 
cargo,  the  first  mate  ft,  and  the  second  mate  |  of 
the  remainder ;  what  part  of  the  whole  does  the 
second  mate  own  ? 

8.  At  the  rate  of  91  miles  an  hour,  how  far  can 
a  boy  ride  on  a  bicycle  in  31  hours  in  the  forenoon 
and  2|  hours  in  the  afternoon  ? 

25.    DIVISION    OF    FRACTIONS. 

Fractions  divided  by  integers. 

Mary  divided  1   of   a   yard  of   ribbon    equally 

among  3  girls;  what  part  of  a  yard  did  each  girl 

receive  ? 

Each  girl  received  £  of  f  of  a  yard,  which  is  J  of  a  yard. 
|  of  a  yard  -f-  3  =  J  of  a  yard. 

16E 


242  ELEMENTARY  ARITHMETIC. 

Divide  i  of  a  cake  equally  between  2  boys ;  what 
part  of  the  cake  does  each  boy  receive  ?  Divide  it 
equally  among  3  boys. 

A  fraction  may  be  divided  by  dividing  the 
numerator  or  by  multiplying  the  denominator. 

What  is  the  fractional  unit 
4  d.  4 

g  -T-  3  =  r  "  =  jz  •  in  the  fraction  |  ?  Multiply- 
ing the  denominator  by  3  has 
what  effect  upon  the  size  of  the  fractional  unit? 
4  fractional  units  of  fifteenths  are  what  part  of  4 
fractional  units  oi fifths? 

26.   Divide: 

1.  J  by  7.  4.  fbylO.  7.    if  by  7. 

2.  {  by  9.  5.  f  by  12.  8.    } f  by  5. 

3.  ?by5.  6.  A  by  6.  9.   Jg  by  3. 

I  of  26*  -  ? 

J  of  26  =  4,  with  a  remainder  of  2.  2  =  Y  +  t  =  V- 
iof^  =  iJ.     iof26i  =  4jJ. 

Note.  Divide  the  integer  and  then  the  fraction,  and  combine  the 
results. 

10.  18}  -T-  6  =  ?  14.  21§  -f-  7  =  ?  18.  14$  -f-  4  =  ? 

11.  20*^5'=?  15.  24J~4  =  ?  19.  33J  -f-  3  =  ? 

12.  26|  -f-  6  =  ?  16.  25}  -f-  5  =  ?  20.  66§  -^  7  =  ? 

13.  32J-f-4  =  ?  17.  463  4-5  =  ?  21.  27§  -f-  7  =  ? 

Note  to  Teachers.  Division  of  Fractions  should  be  taught  both  as 
Partition  and  Division. 

Divide  f  of  a  dollar  equally  among  3  persons. 

This  is  an  example  in  partition.  Each  received  J  of  }  of  a 
dollar,  which  is  \  of  a  dollar. 


DIVISION   OF  FRACTIONS,  243 

At  $3  a  barrel,  how  many  barrels  of  apples  can 

be  bought  for  1  of  a  dollar  ? 

This  is  an  example  in  division.  $3  are  not  contained  in 
|  of  a  dollar.  If  J  of  a  dollar  be  measured  by  $3,  it  will 
be  found  that  |  of  a  dollar  is  J  of  enough  money  to  contain 
$3  once  (or  §  is  J  of  3).  f  ^  3  =  \  (of  1  time).  At  $3  a 
barrel,  J  of  a  barrel  can  be  bought  for  f  of  a  dollar. 

27.  Integers  divided  by  fractions. 

How  many  times  is  \  of  an  orange  contained  in 
2  oranges  ? 

2  oranges  =  |  oranges.     J  is  contained  in  f  eight  times. 

2  ~  I  =  8  (times). 

How  many  times  is  |  of  a  dollar  contained  in 

3  dollars?    ■ 

3  dollars  =  ^  dollars.  \2-  -f- f  =  4  (times),  f  of  a  dol- 
lar is  contained  in  3  dollars  4  times. 

Divide  17  by  f. 

17  =  y.     V  +  1  =  28J  (times). 
Divide : 

1.  18by§.        4.    36  by  J.        7.   54  by  f         10.    16  by  6 J. 

2.  25  by  }.        5.    60  by  |.        8.   56  by  f .         11.    45  by  3 J. 

3.  25  by  £.        6.    71  by  |.        9.   36  by  4J.       12.    28  by  5J. 

Make  a  rule  for  dividing  an  integer  by  a  fraction. 

28.  Fractions  divided  by  fractions. 

How  many  times  is  I  of  a  melon  contained  in  §  ? 
3  in  3  i 

How  many  times  are  |  contained  in  |  ? 


244  ELEMENTARY  ARITHMETIC. 

How  many  times  is  \  of  a  yard  contained  in  \  of 
a  yard  ? 

i  =  t-     I  =  I     I  +  I  =  1*  (times). 
£  of  a  yard  is  contained  in  J  of  a  yard  l£  times. 
Prove  this  by  changing  each  fraction  of  a  yard  to  inches, 
and  then  dividing. 

29.   Divide  1  by  |. 

|  of  the  circle  are  equal  to  how  many 
twentieths  ? 

£  are  equal  to  how  many  twentieths  ? 

£#  contains  ^  how  many  times  ? 

Cut  the  circle  out  of  paper  and  measure 
hi  by  &.     £§  +  &  =  If  (times). 

To  divide  a  fraction  by  a  fraction  : 

Reduce  to  a  common  denominator,  and  divide  the 
numerator  of  the  dividend  by  the  numerator  of  the 
divisor. 

Divide : 

1.  fby|.  4.  fbyj.  7.  £  by  f  10.  2£  by  J. 

2.  fby§.  5.  £by§.  8.  6J  by  h  H-  7  by  J. 

3.  |by§.  6.  At>yf  9.  3ibyf.  12.  9  by  J. 

Inverting  the  divisor. 
Divide  |  by  f. 

|  divided  by  2  equals  §.     The  divisor  is  £  of  2,  and  the 
quotient  must  be  3  times  §,  which  are  §  =  l£.     This  may 
be  expressed  by  "  inverting  the  divisor  " ;  as, 
!  X  I  =  f  =  1£. 

Note  to  Teachers.  This  method  may  be  applied  to  the  explana- 
tion of  examples  in  Division  given  above,  if,  in  the  judgment  of  the 
teacher,  it  is  thought  to  be  of  value  at  this  stage  of  advancement. 


REVIEW.  245 

30.       ORAL  REVIEW. 

1.  The  sum  of  two  fractions  is  %  one  of  the 
fractions  is  \ ;  what  is  the  other  ? 

2.  If  10  oranges  cost  |  of  a  dollar,  what  will  1 
orange  cost  ? 

3.  How  many  badges,  each  ^  of  a  yard  in 
length,  can  I  cut  from  1  of  a  yard  of  ribbon  ? 

4.  A  man  owning  1  of  a  mill  sells  |  of  his 
share ;  what  part  of  the  mill  does  he  still  own  ? 

5.  i  of  a  cord  of  wood  was  sold  for  $4.50;  what 
is  that  a  cord  ? 

6.  f  of  42  is  n  of  what  number  ? 

7.  To  how  many  people  can  you  give  5§  barrels 
of  flour,  if  you  give  \  of  a  barrel  to  each  person  ? 

8.  I  wish  to  put  4f  pounds  of  candy  into  eighth- 
pound  packages.  How  many  packages  can  I 
make? 

9.  At  $8|  a  yard,  what  will  i  of  a  yard  of  velvet 
cost? 

10.  At  1  of  a  dollar  a  yard,  how  many  yards  of 
cloth  can  be  bought  for  $8|  ? 

11.  If  a  jar  holds  i  of  a  gallon  of  fruit,  how 
many  jars  will  be  required  to  hold  6  gallons  ? 

12.  If  3  pounds  of  coffee  are  sold  for  $1,  what 
part  of  3  pounds  should  be  sold  for  25  cents? 
What  part  of  one  pound  ? 


246  ELEMENTARY  ARITHMETIC. 

13.  I  sold  a  book  for  §  of  a  dollar,  which  is  \  of 
a  dollar  less  than  it  cost;  what  part  of  a  dollar 
did  the  book  cost? 

14.  3  oranges  are  sold  for  a  dime  ;  what  must 
I  pay  for  2\  dozen  ? 

15.  If  §  of  a  yard  of  ribbon  cost  25  cents,  what 
will  |  of  a  yard  cost  ? 

16.  How  far  is  it  round  a  field  \  a  mile  long 
arid  I  of  a  mile  wide  ? 

17.  I  of  a  quire  of  paper  made  one  note-book ; 
how  many  quires  will  be  used  in  making  40  such 
books  ? 

18.  Robert  sold  his  sled  for  $lf,  losing  J  the 
cost;  what  did  the  sled  cost? 

19.  A  cake  of  ice  i  of  a  foot  thick  floats  |  above 
the  water ;  what  part  of  a  foot  is  below  the  sur- 
face ?     How  many  inches  ? 

20.  A  boy  bought  f  of  a  bushel  of  chestnuts  for 
$2,  and  sold  them  for  10  cents  a  quart;  how  much 
did  he  gain  ? 

21.  Take  ^  of  a  dollar  from  |  of  a  dollar,  and 
with  the  remainder  buy  oranges  at  |  of  a  dollar  a 
dozen.     How  many  dozen  can  you  buy  ? 

22.  A  man  is  42  years  old,  and  \  of  his  age  is 
|  of  the  age  of  his  son.     How  old  is  his  son  ? 


REVIEW.  247 

23.  Bananas  sell  at  the  rate  of  |  of  a  dozen  for 
J  of  a  dollar.  At  that  rate,  what  will  60  bananas 
cost? 

24.  3  times  |  of  §  is  how  many  times  §  ? 

25.  2J  x  51  =  ?     3)  x  6|  =  ?     6|  —  51  =  ? 

26.  The  difference  between  two  fractions  is  fi. 
One  of  the  fractions  is  | ;  what  is  the  other  ? 

27.  What  will  101  pounds  of  sugar  cost  at  61 
cents  a  pound  ? 

28.  There  are  161  feet  in  one  rod.  How  many 
feet  are  there  in  5  rods  ? 

29.  If  shoes  which  cost  $ 3|  a  pair  are  sold  at 
1  of  the  cost,  how  many  pairs  can  I  get  for  $25  ? 

30.  Horace  earns  $11  a  day.  In  how  many 
days,  at  that  rate,  can  he  earn  $50  ? 

31.     MISCELLANEOUS    PROBLEMS. 

1.  In  three  pieces  of  carpeting  that  contain  44| 
yards,  39|  yards,  and  53^  yards,  how  many  yards? 

2.  A  farmer  sold  two  loads  of  hay,  one  for  $15| 
and  the  other  for  $181,  and  received  $29  down; 
how  much  is  still  due  ? 

3.  Paid  $3651  for  a  horse,  and  sold  him  for  |  of 
what  he  cost ;  what  wTas  the  loss  ? 

4.  Divide  f2  of  21  by  1  of  8f. 

5.  If  a  man  travel  680  miles  in  8|  days,  how 
far  would  he  travel  in  51  days  ? 


248  ELEMENTARY  ARITHMETIC. 

6.  A  miner  digs  16|,  21&,  and  18|  ounces  of 
gold.  He  loses  3i  ounces  in  washing.  How 
much  gold  has  he  left? 

7.  I  earned  $13f  one  week,  $15S  the  next  week, 
$llf  the  next,  and  $18|  the  next;  how  much  did 
I  earn  in  the  four  weeks  ? 

8.  I  sold  a  horse  for  $185?,  and  thereby  lost 
$9jj.     How  much  did  the  horse  cost? 

9.  Bought  47  yards  of  cloth  ;  kept  81  yards,  and 
sold  the  remainder  at  $3J  a  yard.  What  did  I  get 
for  it  ? 

10.  From  240  acres  of  land,  43§  acres  are  sold  to 
one  man,  and  I  of  the  remainder  to  another.  How 
many  acres  remain  unsold  ? 

11.  An  Illinois  farmer  had  three  wheat  fields; 
the  first  produced  219J  bushels,  the  second  407E 
bushels,  the  third  328|  bushels.  He  sent  4581 
bushels  to  a  flour  mill,  and  sold  189  bushels. 
How  many  bushels  were  left  ? 

12.  If  g  of  a  mill  is  worth  $6335,  what  is  three- 
fourths  of  the  remainder  worth  ? 

13.  A  person  spending  1,  f,  and  I  of  his  money 
had  $783  left ;  how  much  had  he  at  first  ? 

14.  If  9|  tons  of  hay  cost  $95,  how  many  tons 
can  be  bought  for  $108  ? 

15.  If  18|  dozen  eggs-cost  $4Jf,  how  much  will 
13!  dozen  cost  ? 


REVIEW.  249 

16.  How  many  pounds  of  butter  at  16f  cents  a 
pound  will  pay  for  24§  pounds  of  sugar  at  6J  cents 
a  pound  ? 

17.  H  +  2|  x  8if  =  ? 

18.  Multiply  1J  4.  2|  by  f  +  4|. 

19.  Find  the  value  of  f  x  2f  -  (If  _  £). 

20.  What  is  the  value  of  f  x  \\  -*-  TV  x  5|  ? 

21.  How  many  weeks  will  it  take  to  spend 
$182,  if  my  weekly  expenses  are  $22£  ?  If  my 
income  is  $37^  a  week,  how  much  do  I  save  in 
that  time  ? 

22.  Bought  a  half  interest  in  a  grocery  for 
$1100.  At  the  end  of  the  year  sold  \  of  my 
interest  for  $500.  What  part  of  the  business  do 
I  still  own  ?  What  is  the  entire  grocery,  or  busi- 
ness, worth  at  that  rate  ? 

23.  The  income  from  my  Iowa  farm  this  year 
is  $4500.  One  ninth  of  this  amount  equals  four 
times  my  income  from  my  orchard.  What  is  the 
income  from  the  latter?  How  many  times  as 
great  is  the  income  from  the  farm  ? 

24.  Mr.  Jones  is  48  years  old.  The  ages  of 
his  wife  and  children  expressed  in  parts  of  his 
age  are  as  follows  :  wife's,  \%  of  his  age ;  John's, 
f  ;  Mary's,  T5g  ;  Susan's,  \  ;  and  Robert's,  \.  What 
is  the  age  of  each?  What  is  the  sum  of  their 
ages  ? 


250  ELEMENTARY  ARITHMETIC. 


CHAPTER  V. 

1.     DECIMAL  FRACTIONS. 

Draw  a  line  upon  the  board  ten  feet  long ; 
divide  it  into  ten  equal  parts.  Each  part  is 
called  what  ? 

Divide  each  tenth  into  ten  equal  parts.  One 
tenth  of  one  tenth  is  what  part  of  the  whole  ? 

One  tenth  of  one  hundredth  is  what  part  of  the 
whole  ? 

One  tenth  of  one  thousandth  is  what  part  of  the 
whole  ? 

How  many  thousandths  make  one  hundredth  ? 

How  many  hundredths  make  one 'tenth  ? 

These  tenth  parts  are  called  decimal  parts. 

A  dime  is  a  decimal  part  of  a  dollar ;  a  cent  is  a  decimal 
part  of  a  dime. 

2.  A  decimal  fraction  is  one  or  more  of  the 
decimal  parts  of  a  unit.  The  denominator  is  ten, 
or  some  power  of  ten. 

3.  In  common  fractions  both  terms  are  written, 
while  in  decimal  fractions  the  denominator  is  indi- 
cated by  the  position  of  the  right  hand  figure  of 
the  numerator  with  respect  to  the  decimal  point. 


DECIMAL   FRACTIONS.  251 

4.  The  decimal  point  is  a  period  placed  at  the 
left  of  the  order  of  tenths  to  indicate  the  decimal 
orders. 

Beginning  with  the  decimal  point,  the  first  place 
to  the  right  is  tenths ;  the  second  place,  hundredths  ; 
the  third  place,  thousandths ;  etc.  The  fraction  & 
is  written  .2 ;  the  fraction  m  is  written  .02. 

2  units. 

.2  tenths. 

.02  hundredths. 

.002  thouscandths. 

.0002  ten-thousandths. 

.00002  hundred-thousandths. 

.000002  millionths. 

5.  In  reading  decimals,  read  the  numbers  as  if 
they  were  integers  (which  gives  the  numerator), 
and  give  the  decimal  order  of  the  last  figure 
(which  gives  the  denominator).  4  tenths  and  5 
hundredths  equal  45  hundredths  (.45).  4  hun- 
dredths and  5  thousandths  equal  45  thousandths 
(.045). 

It  is  best  to  pronounce  the  word  "  and  "  at  the 
decimal  point,  and  omit  it  in  all  other  places  in 
reading  numbers.  200.024  is  read,  two  hundred 
and  twenty-four  thousandths. 

6.  A  mixed  decimal  is  an  integer  and  a  deci- 
mal written  together  as  one  number;  as,  5.02. 


252  ELEMENTARY  ARITHMETIC. 

7.  The  decimal  orders  decrease  in  value  from 
left  to  right,  and  increase  from  right  to  left,  in  the 
same  manner  as  integral  numbers. 


1  il 

JjijSllIlJIlll 

0  0  0  0  0  0  .  0  0  0  0  0  0 


Write  the  decimal  point  and  ciphers  as  given 
above. 

Write  below,  2  in  tenths'  place,  2  in  tens'  place, 
0  in  units'  place,  and  read  the  number. 

Write  6  in  hundreds'  place,  in  units'  place,  and 
in  hundredths'  place,  fill  tens'  and  tenths'  places 
with  ciphers,  and  read  the  number. 

8.  Read  the  following  decimals  : 

.5  .06  .145  3.45  .700 

.05  .60  .265  4.89  4.900 

.15  .56  .103  5.07  4.009 

.30  .84  .047  7.008  6.800 

.45  .96  .006  9.037  6.080 

9.  Express  the  following  in  decimal  form : 

ft*    i%>    Mi    iV*r>    dftft,  Mfei  *ft>  SMtt,  Mjtinr 

6  hundredths.     19  hundredths.     60  thousandths. 
25  hundredths.     40  thousandths.     9  and  7  tenths. 
301  thousandths.   97  hundredths.       6  and  7  hundredths. 

10.  Read  the  following : 

.507  .0030  .5056  .000045 

.0507  .00300  .05056  .000450 

.0336  .03000  .03284  .004500 


DECIMAL   FRACTIONS.  253 

11.  Express  decimally  : 

8  ten-thousandths. 
769  ten-thousandths. 
4004  hundred-thousandths. 

47  millionths. 
3003  hundred-thousandths. 
2364  ten-thousandths. 

3  thousand  and  3  thousandths. 

3  thousand  and  30  thousandths. 

3  thousand  and  300  thousandths. 
Seventeen  and  seventeen  thousandths. 
One  hundred  thousand  and  one  hundred-thousandths. 

^o/V*  too  it?  to ooo?  td%¥W>  Ttf3oV(T0o" J5 j  to~o~8<j0ooo~>  tV°o°o%V> 
r?ft7<nT,  tWo°oV  tVoWoV 

12.  Since  decimal  orders  are  fixed  by  the  deci- 
mal point,  annexing  ciphers  to  a  decimal  does  not 
change  its  value ;  it  is  multiplying  both  terms  of 
the  fraction  by  the  same  number. 

.6  =  .60  (A  =  rtfo). 

Change  2  hundredths  to  thousandths. 

Reduce  .65  to  thousandths ;  95  to  ten-thou- 
sandths. 

Change  .450  to  ten-thousandths ;  450  to  mil- 
lionths. 

Removing  ciphers  from  the  right  of  a  decimal 
does  not  change  its  value. 

Reduce  .3000  to  hundredths;  .3000  to  tenths. 
Change  .16000  to  hundredths;   4.6000  to  hun- 
dredths. 


254  ELEMENTARY  ARITHMETIC, 

13 •     Changing  decimals  to  common  fractions. 
Change  .96  to  a  common  fraction  of  equivalent 
value. 

Write  the  denominator  under  the  decimal,  omit 
the  decimal  point,  and  change  the  fraction  to  its 
lowest  terms. 


Change  to  equivalent  common  fractions  or  mixed 

numbers : 

1.   .9           6.  .275 

11.       .0125 

16.         .0096 

2.   .09           7.    .0275 

12.     5.36 

17.     90.0090 

3.    .35           8.    .045 

13.   15.03G 

18.     60.1600 

4.    .15          9.    .009 

14.   18.005 

19.     19.2576 

5.   .015      10.   .508 

15.   16.16 

20.    180.0008 

X4:«     Changing  common  fractions  to  decimals. 
Change  I  to  an  equivalent  decimal. 

I  =  J8&  reduced  to  hundredths,  f gJHrJ  =  t7^,  which 
expressed  decimally  is  .75. 

The  same  result  is  obtained  by  annexing  ciphers  to  the 
numerator,  dividing  by  the  denominator,  and  pointing  off  as 
many  decimal  places  in  the  quotient  as  there  are  ciphers 
annexed.  4  )  3.00 

.75 

Change  *  to  an  equivalent  decimal. 
6  )  5.000      or,  6  )  5.000 
.833J  .833+ 

If,  after  annexing  ciphers,  the  numerator  is  not  exactly 
divisible  by  the  denominator,  the  decimal  may  be  completed 
by  writing  the  remainder  as  a  common  fraction,  or  the  sign 
+  may  be  added  to  show  that  the  division  is  not  completed. 


DECIMAL   FRACTIONS.  255 

Change  to  equivalent  decimals : 

1.  f,      3.    i,      5.    f,     7.    &,    9.  if»    "-4fei    13-    t>     15.    12&,    17.  16f, 

2.  50f,    4.  62*,    6.  5%,    8.    f,    10.  &,    12.  33*.    14.  jfc,    16.     &,      18.  yfr. 

15.     ADDITION    OF    DECIMALS. 

What  is  the  sum  of  5  tenths  and  3  tenths  ?  8 
tenths  and  9  tenths  ? 

8  tenths  +  9  tenths  =  17  tenths  =  1.7. 

Find  the  sum  of  25.4,  120.7,  216.009,  and  .496. 

25.4 

Write  the  numbers  so  that  units  of  the 

1^^* ■  same  order  stand  in  the  same  column,    Be- 

216.009  gin  at  the  right  and  add  as  in  addition  of 

.496  integers,     Place  the  decimal  point  at  the 

362  605  ^eft  °f  t^ie  tenths'  order  ^n  the  amount. 

Find  the  sum  of : 

(1)  .680,  .729,  .006,  .3,  .40,  and  .400. 

(2)  65.789,  36.908,  45.8,  and  3001.601. 

(3)  8.675,  34.6004,  .0007,  .89070,  and  189.3. 

(4)  1009.09,  3040.60,  10001.345,  .0009,  and  987. 

(5)  62.5  yards  +  95.7  yards  +  67.25  yards  +  9.48  yards. 

(6)  9  and  101  thousandths,  7  and  3  tenths,  15  and  75 
hundredths,  38  and  25  thousandths. 

(7)  One  hundred  eleven  thousandths,  two  hundred  twenty- 
five  ten-thousandths,  sixteen  millionths,  one  hundred  five 
and  one  hundred  five  ten-thousandths,  three  hundred  fifty 
and  three  hundred  fifty  millionths. 

16.     SUBTRACTION    OF   DECIMALS. 

From  45.75  take  26.9. 

45  75  Write  the  subtrahend  under  the  minuend, 

9(\  Q  so  that  units  of  the  same  order  shall  stand 

— : —         in  the  same  column,  and  subtract  as  in  the 
18.85         subtraction  of  integers. 


256  ELEMENTARY  ARITHMETIC. 

From  64.7  take  19.013. 

64.700         If  there  are  more  decimal  places  in  the  sub- 
19.013     trahend  than  in  the  minuend,  fill  the  vacant 
orders  of  the  minuend  with  ciphers. 

Find  the  difference  between : 

(1)  303.48  and  199.09. 

(2)  87.076  and  65.0005. 

(3)  1005.15  and  105.0150. 

(4)  .8  and  .08. 

(5)  9  tenths  and  9  ten-thousandths. 

(6)  101.009  and  81.998. 

(7)  1616.1616  and  987.90. 

(8)  7  hundredths  and  7  millionths. 

(9)  90  hundredths  and  90  thousandths. 

(10)  From  the  sum  of  48.12  and  95.19  take*  60.2. 

(11)  From  the  sum  of  96.009  and  84.325  take  75.0016. 

17.     MULTIPLICATION    OF   DECIMALS. 
Two  times  8  tenths  are  how  many  tenths  ? 
2  times  .8  =  16  tenths  =  1.6. 

3  times  9  tenths  are  how  many  tenths  ? 
A  x  A  =  ?       A  x  Tfo  =  ?       jU  x  Tfo  =  ? 

Express  the  answers  decimally. 

What  is  the  product  when  tenths  are  multiplied 
by  tenths  ?  Hundredths  by  hundredths  ?  Tenths 
by  hundredths  ?     Hundredths  by  thousandths  ? 

Multiply  ft  by  jfc.     Multiply  &  by  i&>. 

Express  answers  decimally. 

The  product  of  thousandths 

iWfr  X  ^  =  tV^jV     -424     by  tenths  is   ten-thousandths. 

.6      The  product  contains  as  many 

.2544     decimal  places  as  there  are  in 

both  factors. 


DECIMAL  FRACTIONS.  257 

18.   Multiply  .253  by  .35. 

ofjo  Multiply  as  in  whole  numbers,  and  point 

off  as  many  decimal  places  in  the  product 

•35       as  there  are  in  both  multiplicand  and  mul- 

1265        tiplier.    If  there  are  not  enough  figures  in 

759  the  product  to  fill  the  decimal  places,  prefix 

as  many  ciphers  as  are  necessary  to  make 

the  required  number. 


.08855 


Multiply  : 

(1)  .386  by  .47  (5)  49..3  by  .064  (9)  376  by  3.06 

(2)  .231  by  .36  (6)  492  by  3.8  (10)  376  by  30.6 

(3)  48.2  by  25  (7)  384.45  by  .64  (11)  .009  by  .009. 

(4)  48.2  by  .25  (8)  38.445  by  .64  (12)  .096  by  .75. 


19.     DIVISION   OP   DECIMALS. 

What  is  the  quotient  of  8  tenths  divided  by  4  ? 
Of  8  tenths  divided  by  4  tenths  ? 

How  many  times  are  3  hundredths  contained  in 
9  hundredths  ?     3  thousandths  in  9  thousandths  ? 

What  is  the  quotient  of  ft  -s-  2  ?    .6  -f  2  =  ? 

What  is  the  quotient  of  ft  +  ft  ?    .6  --  .2  =  ? 

What  is  the  product  of  .7  x  .7  ?    .49  -f-  .7  =  ? 

What  is  the  product  of  .08  x  .08?  .0064  *  .08  =  ? 

2.6  x  4  =  ?         10.4  -5-  4  =  ?         10.4  -  2.6  =  ? 

The  dividend  is  the  product  of  the  divisor  by  the  quo- 
tient. The  quotient  contains  as  many  decimal  places  as 
the  number  of  decimal  places  in  the  dividend  exceeds  the 
number  in  the  divisor. 

17E 


258  ELEMENTARY  ARITHMETIC. 

20.   Divide  16.048  by  3.4.     Divide  9.5  by  .25. 

.25)9.50(38 
7  5 


3.4)16.048(4. 

72 

13  6 

2  44 

2  38 

68 

68 

2  00 

2  00 
9.5  =  950  hundredths  4-  25  hun- 
dredths =  38,  an  integral  number. 

Divide  as  in  the  division  of  integers,  and  point  off 
as  many  decimal  places  in  the  quotient  as  the  number 
of  decimal  places  in  the  dividend  exceeds  the  number 
in  the  divisor. 

Note  1.  When  the  dividend  has  fewer  decimal  places  than  the  divi- 
sor, annex  ciphers  to  the  dividend. 

2.  When  the  quotient  has  not  enough  decimal  figures,  prefix  ciphers. 

3.  When  there  is  a  remainder,  the  division  may  be  continued  by  an- 
nexing ciphers  to  the  dividend. 

21.  Divide: 

(1)  34.5  by  .15  (6)  48.6  by  .02  (11)  .0456  by  9.8 

(2)  34.5  by  .015  (7)  48.6  by  2  (12)  .0656  by  .042 

(3)  5.5  by  1.25  (8)  765  by  .765  (13)  65.65  by  .002 

(4)  5.5  by  .0125  (9)  5.53  by  .0642  (14)  450.5  by  .0175 

(5)  450.5  by  1.75  (10)  2  by  .0002  (15)  86.075  by  25.5 


22.   MISCELLANEOUS  PROBLEMS. 

1,  The  subtrahend  is  eight  thousand  and  forty- 
eight  ten-thousandths,  and  the  remainder  is  eight 
hundred  seventy-three  hundred-thousandths  ;  what 
is  the  minuend  ? 

2.  There  are  228.35  barrels  of  water  in  a  cis- 
tern which  will  hold  410.5  barrels  ;  how  many 
barrels  will  be  needed  to  fill  the  cistern? 


MISCELLANEOUS  PROBLEMS.  259 

3.  At  .085  of  a  dollar  per  dozen,  what  will  lOf 
dozen  steel  pens  cost  ? 

4.  From  a  barrel  containing  43  gallons  of  vine- 
gar, .125  gallons  were  drawn  at  one  time,  3.5  at 
another,  and  .75  at  another;  how  many  gallons 
remained  in  the  barrel  ? 

5.  Dry  goods  valued  at  $8000  were  destroyed 
by  fire ;  what  would  a  man  lose  who  owned  .12 
of  the  goods  ? 

6.  A  gallon,  liquid  measure,  contains  231  cubic 
inches ;  how  many  gallons  in  13051.5  cubic 
inches  ? 

7.  At  $6.80  an  acre,  how  many  acres  of  land 
can  be  bought  for  $4258  ? 

8.  Bought  17  chests  of  tea,  each  containing  59 
pounds,  at  $0.67  a  pound,  and  gave  in  exchange 
118  bags  of  wheat,  each  containing  3.4  bushels; 
what  was  the  value  of  the  wheat  per  bushel  ? 

9.  When  the  dividend  is  .1  and  the  divisor  12.8, 
what  is  the  quotient  ? 

10.  What  is  the  quotient  of  312.5  divided 
by  85? 

11.  If  38  yards  of  cloth  cost  $180.50,  what  will 
be  the  cost  of  26  yards? 

12.  At  $2.56  per  yard,  how  many  yards  of 
cloth  can  be  bought  for  $98.4? 


260  ELEMENTARY  ARITHMETIC. 

13.  A  farmer  sold  to  a  merchant  3  loads  of  hay, 
each  weighing  1876  pounds,  at  $16.50  per  ton 
(2000  pounds),  and  331  bushels  of  oats  at  $0.75 
per  bushel.  He  received  in  payment  32  yards 
of  carpet  at  $0.85  per  yard,  and  23|  yards  of 
matting  at  $0.65  per  yard,  and  the  remainder  in 
money ;    how  much  money  did  he  receive  ? 

14.  A  druggist  sold  375  gallons  of  ink  in  bottles 
holding  .375  of  a  gallon  each ;  how  many  bottles 
of  ink  did  he  sell  ? 

15.  By  selling  a  carriage  for  $195  I  lost  $34.50. 
For  how  much  should  I  have  sold  it  to  gain  an 
amount  equal  to  .7  of  what  I  lost  ? 

23.      UNITED    STATES    MONEY. 

United  States  money  is  the  legal  currency  of 
the  United  States.  Its  denominations  are  dollars, 
dimes,  cents,  and  mills. 

United  States  money  is  based  upon  the  decimal 
system,  —  each  denomination  is  a  decimal  part  of 
a  higher  denomination. 

10  mills  (m.)  =  1  cent. 
10  cents  =  1  dime. 

10  dimes         -=  1  dollar. 

Coin  is  the  metallic  currency  of  the  country- 
Bank  notes  and  United  States  treasury  notes  and 
certificates  are  the  paper  currency. 


UNITED   STATES  MONEY.  261 

The  principal  gold  coins  are  the  double-eagle  ($20),  the 
eagle  ($10),  the  half-eagle  ($5),  the  quarter-eagle  ($2J), 
the  three-dollar  piece,  and  the  dollar. 

The  silver  coins,  5-cent,  10-cent,  25-cent,  50-cent,  and  $1 
pieces. 

The  nickel  coins,  3-cent  and  5-cent  pieces. 

The  bronze  coins,  1-cent  and  2-cent  pieces. 

There  is  no  coin  known  as  the  mill.  That  denomination 
is  used  only  in  making  calculations. 

24.  The  rules  which  apply  to  calculations  in- 
volving integers  and  decimals  apply  also  to  calcu- 
lations involving  United  States  money. 

Dollars  and  cents  are  separated  by  the  decimal 
point.  The  two  figures  at  the  right  of  dollars 
express  cents,  and  the  third  figure  expresses  mills. 

Read  the  following : 

$4,605  $3,078  $8,707  $0,005 

$4,065  $7,077  $7,007  $0,095 

25.  Express  in  figures: 

1.  Twenty-five  dollars  five  mills. 

2.  Nine  dollars  one  cent  one  mill. 

3.  Seventeen  dollars  seventeen  cents. 

4.  Seven  dollars  one  cent  seven  mills. 

5.  Twelve  dollars  seven  and  a  half  cents. 

6.  One  hundred  eleven  dollars  one  cent  one  mill. 

7.  One  thousand  one  dollars  one  mill.     * 

8.  Two  thousand  dollars  two  and  a  half  cents. 


262  ELEMENTARY  ARITHMETIC. 

26.   Reduce  $18.00  to  cents. 
One  dollar  equals  one  hundred  cents. 
1 18  =  18  times  100  cents  =  1800  cents. 

To  reduce  dollars  to  cents : 

Annex  two  ciphers  and  remove  the  dollar  sign. 

Reduce  $18.75  to  cents. 

$18  =  1800  cents.     1800  +  75  cents  =  1875  cents. 

To  reduce  dollars  and  cents  to  cents : 
Remove  the  decimal  point  and  the  dollar  sign. 

Reduce  to  cents:  $29;  $72.75;  $30.16;  $200.02. 

Reduce  80  cents  to  mills. 

1  cent  equals  10  mills.     80  cents  =  80  times  10  mills 
r=  800  mills. 

To  reduce  cents  to  mills : 
Annex  one  cipher. 

Reduce  $9  to  mills. 

One   dollar  =  1000   mills.      $9  =  9  times  1000  mills 
e=  9000  mills. 

To  reduce  dollars  to  mills  : 

Annex  three  ciphers  and  remove  the  dollar  sign. 

To  reduce  dollars,  cents,  and  mills  to  mills : 
Remove  the  decimal  point  and  the  dollar  sign. 

Reduce  the  following  to  mills  : 

1.  $34  5.  $24,655  9.  $18,964  13.  $13,145 

2.  $25.25  6.  $9.12£  10.  $0.75  14.  $0,755 

3.  $0,535  7.  $0,672  11.  $0.37|-  15.  $8.62£ 

4.  $0.98  8.  $100.75  12.  $1000.62  16.  $46,024 


UNITED   STATES  MONEY.  263 

27.    Reduce  1800  cents  to  dollars. 

One  dollar  equals  100  cents.  In  1800  cents  there  are  as 
many  dollars  as  there  are  100  cents  in  1800  cents,  or  $18. 

To  reduce  cents  to  dollars : 

Divide  by  one  hundred,  by  placing  the  decimal  point 
before  the  second  figure  from  the  right. 

To  reduce  mills  to  dollars: 

Divide  by  one  thousand,  by  placing  the  decimal 
point  before  the  third  figure  from  the  right. 

Reduce  to  dollars : 

1.  1200  cents;  2.  12000  cents;  3.  29018  cents; 
,4.  160  cents;  5.  1200  mills;  6.  2500  mills; 
7.   25000  mills. 

28.     ADDITION   AND    SUBTRACTION. 

To  add  or  subtract  United  States  money : 

Write  units  of  the  same  order  in  the  same  column^ 
and  add  or  subtract  as  in  simple  numbers.  Separate 
dollars  and  cents  by  the  decimal  point. 

1.  What  is  the  sum  of  $34,  $15.85,  $6,875, 
$0.95,  and  $0,621? 

2.  Find  the  sum  of  $11.93,  $119,  $4007.62, 
and  $30.09. 

3.  From  $62.40  take  $7,371.    ($7,371=  $7,375.) 

4.  From  $892.46  take  $495.78. 

5.  From  $500.63  take  $199.73. 


264  ELEMENTARY  ARITHMETIC. 

29.     MULTIPLICATION   AND   DIVISION. 

What  will  50  bushels  of  wheat  cost  at  $1.62|  a 

bushel  ? 

$1,625 
50 

$81,250 

At  $ 0.12|  a  box,  how  many  boxes  of  pens  can 
be  bought  for  $6.00? 

$0,125  )  $6,000  (  48  (times). 
5  00 

1  000  Arts.   48  boxes. 

1000       • 

When  the  dividend  has  fewer  decimal  places  than  the 
divisor,  annex  ciphers  to  the  dividend. 

If  7  barrels  of  cider  can  be  bought  for  $35.87i, 
what  is  the  cost  of  one  barrel  ? 

7 )  $35.875 

$5,125    Ans. 

To  multiply  or  divide  sums  of  money  i 

Multiply  or  divide  as  in  integers  and  decimals. 
Separate  dollars  and  cents  in  the  result  by  the  deci- 
mal point. 

30.     MISCELLANEOUS    PROBLEMS. 

1.  From  the  sum  of  $15.75  and  $1001.10  take 
the  sum  of  $101,018  and  $50,101. 

2.  Subtract  $0.50  from  $1,005. 


MISCELLANEOUS  PROBLEMS.  265 

3.  A  man  bought  a  coat  for  $16,  a  vest  for 
$3.50,  and  a  pair  of  trousers  for  $5.50  ;  what 
two  coins  will  exactly  pay  for  them? 

4.  From  the  sum  of  $14.50  and  $12.75  take  6 
dimes  6  mills. 

5.  From  $4.50  take  371  cents. 

6.  A  grocer  bought  3  barrels  of  apples  for 
$6.75,  a  box  of  lemons  for  $2.50,  and  5  barrels 
of  flour  for  $30.00.  He- handed  the  merchant 
two  gold  pieces,  and  received  $0.75  in  change. 
What  were  the  two  pieces  of  money? 

7.  At  $0,121  a  yard,  how  much  muslin  can  be 
bought  for  $20.43  ? 

8.  If  i  of  a  yard  of  cloth  cost  $2.16,  what  will 
be  the  cost  of  51  pieces,  each  containing  447  yards  ? 

9.  When  rice  is  selling  at  $.075  a  pound,  how 
many  pounds  can  be  bought  for  $5.25  ? 

10.  How  many  days,  of  9  hours  each,  must  a 
man  work  in  order  to  earn  $576.72,  at  18  cents 
an  hour? 

11.  If  a  lady  earns  $15.00  a  week,  and  spends 
an  average  amount  of  $11,371?  in  how  many  weeks 
will  she  save  $166.75? 

12.  31.5  gallons  of  vinegar  cost  $11.81^;  how 
much  is  that  per  gallon  ? 


266  ELEMENTARY  ARITHMETIC. 

BILLS. 

13.  Thomas  Wilson  bought  of  James  Mitchell 
&  Son,  St.  Louis,  Mo.,  Sept.  8,  1890,  18  yards  of 
flannel,  at  36  cents;  15  yards  of  muslin,  at  23 
cents ;  3  dozen  silk  buttons,  at  42  cents  ;  18  yards 
of  sheeting  at  16£  cents;  2  boys'  suits,  at  $8.50 
and  $13;  3  silk  ties,  at  85  cents;  1  cloak,  $16.50; 
I  dozen  handkerchiefs,  at  18  cents  each ;  13  yards 
of  velvet,  at  $2.75.  Make  out  and  receipt  this 
bill  as  clerk  of  James  Mitchell  &  Son. 

14.  John  Clark  bought  of  Charles  Andrews,  De- 
troit, Mich.,  Aug.  12,  1890,  13  yards  of  silk,  at 
$2.95;  6  pairs  of  kid  gloves,  at  $1.49  ;  33^  yards 
of  drilling,  at  18  cents  ;  19  yards  of  ribbon,  at  36 
cents;  1  dozen  linen  napkins,  at  $3.75;  1  over- 
coat, $23.75;  1  umbrella,  $3.75;  1%  yards  of 
cambric,  at  14  cents ;  6^  yards  of  embroidery,  at 
48  cents.     Make  out  and  receipt  this  bill. 

15.  James  Goodman  bought  of  C.  H.  Slack  & 
Co.,  Chicago,  111.,  April  19,  1893,  5  barrels  of  flour, 
at  $7.50;  2  barrels  of  brown  sugar,  270  pounds 
each,  at  4  cents ;  1  barrel  of  granulated  sugar,  225 
pounds,  at  6  cents ;  1  sack  of  coffee,  60  pounds,  at 
22J  cents ;  2  boxes  of  raisins,  each  18  pounds,  at 
9  cents;  1  chest  of  tea,  37  pounds,  at  37|  cents. 
Make  out  and  receipt  this  bill. 


COMPOUND  NUMBERS.  267 


CHAPTER  VI. 

COMPOUND    NUMBERS. 

1.  A  Simple  Quantity  is  expressed  in  units  of 
one  denomination ;  as,  4  pecks. 

A  Compound  Quantity  is  expressed  in  units  of 
different  denominations  which  are  reducible  to 
units  of  the  same  denomination ;  as,  4  pecks, 
3  quarts. 

2.  A  Denominate  Number  is  a  number  com- 
posed of  denominate  units. 

A  Simple  Denominate  Number  is  composed  of 
units  of  one  denomination. 

A  Compound  Denominate  Number  is  composed 
of  units  of  two  or  more  denominations  which  are 
reducible  to  units  of  the  same  denomination. 

3.  Reduction  is  the  process  of  changing  the 
denomination  of  a  number  without  changing  its 
value.  Changing  denominate  numbers  to  lower 
denominations  is  called  Reduction  Descending. 
Changing  to  higher  denominations  is  called  Re- 
duction Ascending. 

In  reducing  denominate  numbers,  the  increase  or  decrease 
in  the  number  of  units  is  by  an  irregular  scale,  instead  of  by 
the  decimal  scale  as  in  simple  numbers. 


268  ELEMENTARY  ARITHMETIC. 

DRY    MEASURE. 

4.  Dry  Measure  is  used  in  measuring  grain, 
fruit,  seeds,  vegetables,  and  other  dry  articles. 

The  denominations  are  pints,  quarts,  pecks,  and 

bushels. 

2  pints  (pt.)  =  1  quart  (qt.). 
8  quarts  =  1  peck  (pk.). 
4  pecks  =  1  bushel  (bu.). 

1  bu.  as  32  qt.  =  64  pt. 

The  standard  bushel  is  18J  inches  in  diameter  and  8 
inches  deep,  and  contains  2150.42  cubic  inches. 

1.  How  many  bushels  in  24  pecks?  25  pecks? 
35  pecks  ? 

2.  Reduce  5  bushels  to  pecks.     To  quarts. 

3.  Reduce  2  pecks  to  pints.     2  bushels  to  pints. 

5.  Reduce  16  bu.  3  pk.  1  pt.  to  pints. 

One  bushel  =  4  pecks.  In  16  bush- 
els there  are  4  times  as  many  ones  of 
pecks  as  ones  of  bushels.  16  multi- 
plied by  4  =  64.  There  are  64  pecks 
in  16  bushels.  64  pecks  +  3  pecks 
=  67  pecks. 

One  peck  =  8  quarts.     In  67  pecks 
1073  pt.  there    are    8    times    as    many    quarts. 

8   times   67  =  536.      There    are    536 
quarts  in  67  pecks. 

One  quart  =  2  pints.  In  536  quarts  there  are  2  times  as 
many  pints.  2  times  536  =  1072.  1072  pints  +  1  pint 
=  1073  pints. 

16  bushels,  3  pk.  1  pt.  =  1073  pints.    Ans. 


bu.     pk. 

16    3 

qt.     pt. 

0    1 

4 

67  pk. 

8 

536  qt. 
2 

DRY  MEASURE.  269 

1.  Reduce  8  bu.  3  pk.  1  pt.  to  pints. 

2.  Reduce  15  bu.  3  pk.  to  quarts. 

3.  Reduce  12  bu.  1  pk.  3  qt.  to  pints. 

4.  Reduce  3  pk.  6  qt.  to  pints. 

To  reduce  a  compound  denominate  number  to  a 
lower  denomination  : 

Multiply  the  highest  denomination  by  the  number 
of  ones  of  the  next  lower  which  make  one  of  the  higher, 
and  add  to  the  product  the  given  number  of  the  same 
deno  mination. 

Proceed  in  like  manner  with  each  successive  result, 
until  the  number  is  reduced  to  the  required  denomi- 
nation. 

6.    Reduce  689  pints  to  bushels. 

9 .  fi£  There  are  in  689  pints  as  many 

' *  quarts  as  there  are  times  2  pints, 

8  )  344  qt.  +  1  pt.        wMcll  is  344)  with  jl  pint  remain. 

4)43  pk.  ing  un(jivided. 

10  bu.  +  3  pk.  There    are    in    344    quarts    as 

many   pecks    as    there   are   times 
8  quarts,  which  is  43. 

There  are  in  43  pecks  as  many  bushels  as  there  are  times 
4  pecks,  which  is  10,  with  3  pecks  remaining. 
689  pints  ==  10  bu.  3  pk.  1  pt. 

1.  Reduce  817  pints  to  bushels.  168  quarts  to 
bushels. 

2.  Reduce  682  pints  to  bushels.  95  pints  to 
pecks. 

3.  Reduce  125  quarts  to  bushels.  87  pints  to 
pecks. 


270  ELEMENTARY  ARITHMETIC. 

To  reduce  a  compound  denominate  number  to  a 
higher  denomination  : 

Divide  the  given  number  by  the  number  of  ones  tliat 
make  one  of  the  next  higher  denomination. 

Divide  this  quotient  and  each  successive  quotient 
in  like  manner,  until  the  required  denomination  is 
reached. 

The  last  quotient,  with  the  several  remainders  an- 
nexed, in  proper  order,  is  the  result  required. 

LIQUID    MEASURE. 

7.   Liquid  Measure  is  used  in  measuring  liquids. 

The    denominations   are   gills,  pints,  quarts,  and 

gallons. 

4  gills  (gi.)  =  1  pint  (pt.). 
2  pints  =  1  quart  (qt.). 

4  quarts       =  1  gallon  (gal.). 

The  gallon  contains  231  cubic  inches,  lj  pints  liquid 
measure  equal  1  pint  dry  measure. 

The  barrel  contains  31 J  gallons;  the  hogshead  63  gallons. 

1.  Reduce  15  gallons  to  pints.  Reduce  18 
gallons  to  gills. 

2.  Reduce  17  gal.  1  qt.  1  pt.  3  gi.  to  gills.  Re- 
duce 8  quarts  to  gills. 

3.  How  many  gallons  in  47  quarts?  How 
many  gallons  in  47  pints  ? 

4.  Reduce  86  gills  to  quarts.    98  gills  to  gallons. 

5.  Reduce  25  gal.  1  pt.  to  gills.  Reduce  19 
gallons  to  pints. 


AVOIRDUPOIS    WEIGHT.      TROY    WEIGHT.     271 

AVOIRDUPOIS    WEIGHT. 

8.  Avoirdupois  Weight  is  used  in  weighing  all 
articles  except  gold,  silver,  and  precious  stones.  The 
denominations  are  ounces,  pounds,  hundred-weights, 
and  tons. 

16  ounces  (oz.)  =  1  pound  (lb.)- 

100  pounds  =  1  hundred-weight  (cwt.), 

20  hundred-weight,  2000  lb.    =  1  ton  (T.). 
60  pounds  of  wheat  ==  1  bushel. 

56        "  corn  or  rye   =1      " 

32         "  oats  =1      " 

100         "  nails  =  1  cask  or  keg. 

196         "  flour  =  1  barrel. 

200         "  beef  or  pork  =  1  barrel. 

1.  Reduce  3  tons  to  pounds.  Reduce  6  hun- 
dred-weight to  ounces. 

2.  Reduce  7  cwt.  48  lb.  9  oz.  to  ounces.  Reduce 
9  tons  to  ounces. 

3.  Reduce  54145  pounds  to  tons.  Reduce  3684 
ounces  to  pounds. 

4.  Reduce  36425  pounds  to  hundred-weights. 
Reduce  32000  ounces  to  tons. 

5.  Reduce  5  T.  12  cwt.  36  lb.  to  pounds. 

TROY    WEIGHT. 

9.  Troy  Weight  is  used  in  weighing  gold,  sil- 
ver, and  jewels. 

24  grains  (gr.)      =  1  pennyweight  (pwt). 
20  pennyweights  =  1  ounce  (oz.). 
12  ounces  =  1  pound  (lb.). 


272  ELEMENTARY  ARITHMETIC. 

10.     MISCELLANEOUS   PROBLEMS. 

1.  How  many  pint  packages  can  a  seedsman 
make  from  4  bu.  2  pk.  and  2  qt.  of  seeds  ? 

2.  What  will  \\  barrels  of  vinegar  cost  at  8 
cents  a  quart? 

3.  In  one  season  a  market-gardener  sold  12345 
boxes  of  strawberries,  averaging  1  quart  each. 
How  many  bushels  did  he  sell  ? 

4.  At  7  cents  a  pound,  what  will  2|  barrels  of 
pork  cost  ? 

5.  If  a  horse  eats  1  pk.  6  qt.  of  oats  in  a  day, 
how  long  will  7  bu.  2  pk.  last  ? 

LONG    MEASURE. 
11.   Long  or  Linear  Measure  is  used  in  meas- 
uring lengths  and  distances. 

The  denominations  are  inches,  feet,  yards,  rodsy 
and  miles. 

12    inches  (in.)  =  1  foot  (ft.). 

3    feet  =  1  yard  (yd.). 

h\  yards,  or  16£  feet    =  1  rod  (rd.). 
320    rods  s  1  mile  (mi.). 

1760    yards,  or  5280  feet  =  1  mile. 

1.  Reduce  12  rods  to  feet.  Reduce  15  rd.  3  yd. 
2  ft.  to  feet. 

2.  Reduce  136  rd.  4  yd.  to  inches.  Reduce  18 
miles  to  rods. 

3.  Reduce  4  mi.  130  rd.  to  rods.  Reduce  5  mi. 
20  rd.  to  inches. 


SQUARE  MEASURE  273 

4.  Change  to  lowest  denominations :  2|  miles ; 
16  rd.  25  ft. ;   34  yd.  ;   16.8  rd.  32|  yd.  18|  ft. 

5.  Change  to  highest  denominations :  16000 
feet;  63360  inches;  3240  rd.;  7040yd.;  47520  ft. 

6.  Measure  one  side  of  your  school  lot  and  give 
the  length  in  rods. 

7.  How  many  rods  in  \  of  a  mile  ? 

8.  40  rods  is  what  part  of  a  mile  ? 

9.  If  the  large  wheel  of  a  bicycle  is  15  feet  in 
circumference,  how  many  times  will  it  turn  in 
going  5  mi.  182  rd.  4  yd  ? 

10.  In  a  bundle  of  lath  there  are  100  pieces  each 
4  feet  long.  If  all  the  pieces  of  the  4  bundles  were 
laid  end  to  end,  what  would  be  the  length  in  rods  ? 

11.  From  A  to  B  is  17  rods.  How  many  feet 
in  one  third  that  distance  ? 

12.  How  long  will  it  take  George  to  walk,  a 
half-mile,  if  he  walks  at  the  rate  of  20  rods  a 
minute  ? 

SQUARE    MEASURE. 

12.  Square  Measure  is  used  in  measuring  sur- 
faces, as  of  land,  boards,  plastering,  etc. 

The  denominations  are  square  inches,  square  feet, 

square  yards,  square  rods,  and  square  miles. 

144    square  inches  (sq.  in.)  =1  square  foot  (sq.  ft.). 
9    square  feet  =  1  square  yard  (sq.  yd.). 

30^  square  yards  =  1  square  rod  (sq.  rd.). 

160    square  rods  =  1  acre  (A.). 

640    acres  =  1  square  mile  (sq.  mi.). 


274  ELEMENTARY  ARITHMETIC. 

13.  A  surface  has  two  dimensions,  length  and 
breadth. 

A  plane  surface  which  has  four  square  corners 
is  called  a  rectangle. 

A  rectangle  which  has  four  equal  sides  is  called ' 
a  square.' 

The  area  of  a  surface  is  the  number  of  square 
units  it  contains. 

Suppose  the  top  of  a  table  to  be  4  feet  long  and  2  feet 
wide.  There  are  two  rows  of  4  square 
feet  each;  that  is,  2  times  4  square  feet 
or  8  square  feet  in  the  surface  of  the 
table.  The  width  of  one  end  shows 
how  many  times  4  square  units  must 
be  taken  to  give  the  whole  area. 

To  find  the  area  of  a  rectangular  srirface,  a  certain  num- 
ber of  square  units  are  taken  a  given  number  of  times. 

What  is  the  length  of  one  side  of  a  square  yard  ? 

Measure  off  in  your  schoolyard  a  square  rod. 
What  is  the  length  of  each  side  ? 

What  is  the  area  of  a  square  that  is  5h  yards  on 
each  side  ? 

To  find  the  area  of  a  rectangular  surface  : 

The  length  and  breadth  being  given  in  the  same 
denomination,  multiply  the  length  by  the  breadth* 

14.  Reduce  to  lower  denominations  : 

1.  140  square  rods  to  square  feet. 

2.  18  acres  t    square  rods. 


PROBLEMS.  275 

3.  12  A.  50  sq.  rd.  8  sq.  yd.  1  sq.  ft.  to  square 
feet. 

4.  1  square  mile  to  square  inches. 

5.  112  sq.  rd.  5  sq.  ft.  to  square  feet. 

Reduce  to  higher  denominations  : 

6.  1440  square  rods  to  acres  ;  4320  square  rods 
to  acres. 

7.  23328  square  inches  to  square  yards. 

8.  10890  square  feet  to  square  rods. 

9.  102400  sq.  rd.  to  square  miles. 

10.  5760  A.  to  square  miles. 

15.     PROBLEMS. 

1.  How  many  square  inches  of  surface  has  a 
pane  of  glass  3  feet  long  and  2  feet  wide  ?  (Make 
a  drawing  to  show  the  number  of  rows  of  square 
feet ;  the  number  of  rows  of  square  inches.) 

2.  How  many  square  inches  in  f  of  a  square 
foot?     In   |  of  a  square  foot?     (Drawing.) 

3.  How  many  square  inches  of  surface  in  the 
top  of  a  table  which  is  3  feet  long  and  2\  feet 
wide  ? 

4.  Find  the  area  of  a  floor  which  is  12  feet  by 
15  feet. 

5.  A  floor  has  a  surface  of  180  square  feet ;  if 
its  length  is  15  feet,  what  is  its  width  ? 


276 


ELEMENTARY    ARITHMETIC. 


6.  How  many  acres  in  a  field  18  rods  long  and 
9  rods  wide  ? 

7.  At  $48  an  acre,  what  will  be  the  cost  of  a 
piece  of  land  160  rods  long  and  118  rods  wide  ? 

CUBIC    MEASURE. 

16.  Cubic  Measure  is  used  in  measuring  solids. 
Its  denominations  are  cubic  inches,  cubic  feet,  cubic 
yards,  and  cords. 

1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.). 

128  cubic  feet  =  1  cord  (cd.). 

In  measuring  wood,  a  pile  8  feet  long,  4  feet  wide,  and 
4  feet  high  is  called  a  cord. 

17.  A  cube  is  a  solid  bounded  by  six  equal 
squares. 

A  cubic  foot  is  a  cube  whose  faces  are  each  one 
foot  square. 

The  solid  contents  of  a  body  is  the  number  of 
cubic  units  it  contains. 

The  base  of  this  cube  is  di- 
vided into  square  feet.  There 
are  3  rows  of  3  square  feet 
each,  making  in  all  3  times  3 
square  feet,  which  are  9  square 
feet. 

If  upon  each  square  foot  we  place  3  cubic  feet, 
we  shall  have  9  times  3  cubic  feet,  which  are  27 
cubic  feet. 


3    Ft 


CUBIC  MEASURE. 


211 


A  solid  which  is  3  feet  long,  3  feet  wide,  and 
3  feet  high  is  a  cubic  yard,  and  contains  27  cubic 
feet. 

How  many  cubic  feet  in  \  of 
a  cubic  yard  ? 

How  many  cubic  feet  in  I  of 
a  cubic  yard  ? 

How  many  cubic  feet  in  I  of 
a  cubic  yard?  »m.&x8.^il 

To  find  the  number  of  cubic  units  in  any  rectan- 
gular solid : 

The  length,  breadth,  and  height  being  given  in  the 
same  denomination,  their  product  is  the  number  of 
cubic  units,  of  the  same  name  as  the  linear  units. 


18.  How  many  cubic  feet 

of  ^inrl  will   bp  rpnnired   to      ■^"^                             ' 

fill  this  box  ? 

How  many  cubic  feet  in 

£ 

a  layer  of  sand  1  foot  high 

*i 

sr 

in  this  box  ? 

4-  Fr- 

How  many  cubic  inches  in  one  cubic  foot  ?  How 
many  square  inches  of  surface  has  one  of  the  faces  ? 

Build  the  cubic  foot  of  1-inch  cubes. 

These  surface  units  are  faces  of  what  cubic 
units? 

How  many  times  must  144  cubic  inches  be  taken 
to  make  one  cubic  foot  ? 


278  ELEMENTARY  ARITHMETIC. 

19.      PROBLEMS. 

1.  How  many  cubic  inches  in  1  cubic  yard  ? 
In  I  of  a  cubic  yard  ?     In  §  of  a  cubic  yard  ? 

2.  Reduce  12  cubic  feet  to, cubic  inches. 

3.  Reduce  87  cubic  yards  to  cubic  feet;  62| 
cubic  yards  to  cubic  feet. 

4.  Reduce  16  cords  to  cubic  feet ;  10J  cords  to 
cubic  feet. 

5.  Reduce  20736  cubic  inches  to  cubic  feet. 

6.  Reduce  540  cubic  feet  to  cubic  yards. 

7.  Reduce  9  cu.  yd.  7  cu.  ft.  to  cubic  inches. 

8.  Reduce  18  cu.  yd.  12  cu.  ft.  720  cu.  in.  to 
cubic  inches. 

9.  Reduce  1152  cubic  feet  to  cords ;  6400  cubic 
feet  to  cords. 

10.  How  many  cubic  feet  in  a  rectangular 
block  of  stone  8  feet  long,  5  feet  wide,  and  3  feet 
thick?     (Make  a  drawing  to  show  this.) 

11.  How  many  cubic  feet  in  a  pile  of  bricks  8 
feet  long,  4  feet  wide,  and  4  feet  high  ? 

12.  A  tank  6  feet  long,  5  feet  wide,  and  3  feet 
deep  contains  how  many  cubic  inches  ? 

13.  How  many  cubic  feet  of  air  in  a  room  18 
feet  long,  15  feet  wide,  and  10  feet  high? 


TIME  MEASURE.  279 

14.  In  digging  a  cellar  16  feet  long,  12  feet 
wide,  and  8  feet  deep,  how  many  cubic  feet  of 
earth  must  be  removed? 

15.  How  many  cords  in  a  pile  of  wood  16  feet 
long,  5  feet  high,  and  4  feet  wide  ? 

16.  At  $27  a  cubic  yard,  what  will  it  cost  to 
dig  a  cellar  18  feet  long,  14  feet  wide,  and  9  feet 
high? 

17.  How  many  cubic  feet  in  a  stick  of  timber  18 
inches  wide,  8  inches  thick,  and  12  feet  long  ? 

18.  What  is  the  value  of  a  pile  of  wood  82  feet 
long,  4  feet  wide,  and  5  feet  high,  at  $4.50  a  cord  ? 

TIME   MEASURE. 

20.    Time  Measure  is  used  in  measuring  time. 
The  denominations  are  seconds,  minutes,  hours, 
days,  weeks,  months,  years,  and  centuries. 

60  seconds  (sec.)  =  1  minute  (min.). 

60  minutes  =  1  hour  (h.). 

24  hours  =  1  day  (d.). 

7  days  ==  1  week  (wk.). 

365  days  =  1  year  (yr.). 

366  days  =  1  leap  year  (1.  yr.). 
100  years  =  1  century  (C). 

February  has  28  days,  except  in  leap  year,  when  it  has  29. 

September,  April,  June,  and  November,  each  have  30 
days;  other  months  of  the  year  (except  February)  each 
have  31  days. 

In  business  transactions  12  months  are  considered  a 
year  and  30  days  a  month. 


280  ELEMENTARY  ARITHMETIC. 

21.    Reduce  to  lower  denominations  : 

1.  12  hours  to  seconds  ;  5  days  to  minutes. 

2.  8  d.  12  h.  40  min.  to  seconds. 

3.  How  many  minutes  in  the  month  of  Feb- 
ruary, 1892  (1.  yr.)  ? 

Reduce  to  higher  denominations : 

4.  1440  minutes  to  days;  86400  seconds  to 
days. 

5.  52560  hours  to  years;  4743856  minutes  to 
years. 

22.     MISCELLANEOUS    MEASURES. 

PAPER.  COUNTING. 

24  sheets     =  1  quire  (qr.).  12  things  =  1  dozen  (doz.). 

20  quires     =  1  ream.  12  dozen    =  1  gross  (gro.). 

2  reams     =  1  bundle.  12  gross    =  1  great  gross. 

5  bundles  =  1  bale. 

ADDITION    OF    COMPOUND    NUMBERS. 
23.    What  is  the  sum  of  4  gal.  3  qt.  1  pt.,  6  gal. 
1  qt.,  7  gal.  2  qt.  1  pt.  ? 

Write  like  denominations  in  the  same 
column,  and  begin  with  the  lowest  denomi- 
nation to  add. 

1  pint  and  1  pint  are  2  pints,  equal  to  1 
18     3     0      qUart)  which  we    add  with   the   column  of 
quarts,  writing  0  under  the  column  of  pints. 

1  quart,  2  quarts,  1  quart,  and  3  quarts  are  7  quarts, 
which  are  equal  to  1  gallon,  3  quarts.  We  write  three 
under  the  column  of  quarts,  and  add  the  1  gallon  with  the 
column  of  gallons. 

1  gallon,  7  gallons,  6  gallons,  and  4  gallons  are  18  gal- 
lons, which  we  write  under  the   column  of  gallons 


gal. 

qt. 

pt. 

4 

3 

1 

6 

1 

0 

7 

2 

1 

COMPOUND   NUMBERS.  281 

1.  Add  14  bu.  2  pk.  5  qt.  1  pt.,  12  bu.  1  pk. 
4  qt.,  30  bu.  3  pk.  1  pt.,  and  18  bu.  2  qt. 

2.  What  is  the  sum  of  18  mi.  316  rd.  4  yd.  2  ft. 

11  in.,  29  mi.  112  rd.  5  yd.  1  ft.  5  in.,  19  mi.  142 
rd.  8  in.,  and  9  mi.  16  rd.  3  yd.  1  ft.  ? 

3.  Add  14  w.  9  d.  11  h.  34  min.  34  sec,  8  w. 
8  d.  16  h.,  11  w.  30  h.  40  min.,  17  d.  21  h.  45  min. 
16  sec,  and  2  w.  3  d.  3  h.  25  min. 

4.  What  is  the  sum  of  12  gal.  3  qt.  1  pt.  3  gi., 

13  gal.  1  pt.  2  gi.,  25  gal.  2  qt.,  and  18  gal.  1  pt.  3  gi.? 

SUBTRACTION   OP   COMPOUND   NUMBERS. 

24.   From  28  rd.  5  yd.  1  ft.  take  9  rd.  3  yd. 

2  ft. 

Write  like  denominations  in  the  same  col- 
umn and  begin  with  the  lowest  to  subtract. 
2  feet  cannot  be  taken  from  1  foot.    Take 
ly     1     J      -j_  yard  from  5  yards,  reduce  it  to  feet,  and 
add  it  to  1  foot.     2  feet  from  4  feet  leaves  2  feet.     3  yards 
from  4  yards  leaves  1  yard.     9  rods  from  28  rods  leaves  19 
rods. 

1.    From  38  gal.  3  qt.  1  pt.  2  gi.  take  27  gal. 

3  qt.  3  gi. 

2.  From  53  cwt.  63  lb.  9  oz.  take  33  cwt.  64  lb. 

14  oz. 

3.  From  18  w.  1  d.  8  h.  45  min.  take  7  w.  5  d. 

12  h.  36  min. 


rd. 

yd. 

ft. 

2$ 

5 

1 

9 

3 

2 

282  ELEMENTARY  ARITHMETIC. 

4.  What  is  the  difference  in  time  between 
Dec.  25,  1876,  and  Oct.  12,  1892? 

y*       mo-     d-  Write  the  earlier  date   (1876,    12th 

1892     10     12      montn>  25th  day)  under  the  later  (1892, 

1876     12     25      10th   ^onth,   12th   day)   and   subtract, 

15       9     17      allowing   30  days  to  a  month  and    12 

months  to  a  year. 

5.  What  is  the  difference  in  time  between  July 
4,  1876,  and  Jan.  1,  1892? 

MULTIPLICATION    OF    COMPOUND    NUMBERS. 

25.    Multiply  120  mi.  90  rd.  2  ft.  7  in.  by  5. 

Five  times  7  inches  are  35  inches, 
equal  to  2  feet  and  11  inches.  Write 
11  in  the  place  of  inches,  and  add  2 
feet  to  the  product  of  feet. 

5  times  2  feet  are  10  feet,  and 
2  feet  added  are  12  feet.  12  feet  equal  4  yards.  Write 
0  in  the  place  of  feet,  and  add  4  yards  to  the  product  of 
yards. 

The  product  of  0  yards  multiplied  by  5  is  0.  Write  4 
in  the  place  of  yards. 

5  times  90  rods  are  450  rods,  equal  to  1  mile  and  130 
rods.  Write  130  in  the  place  of  rods,  and  add  1  mile  to  the 
product  of  miles. 

5  times  120  miles  are  600  miles,  and  1  mile  added  are 
601  miles. 

Multiply  : 

1.  50  mi.  30  rd.  4  yd.  7  in.  by  9. 

2.  5  gal.  3  qt.  2  gi.  by  12. 

3.  6  T.  3  cwt.  14  lb.  9  oz.  by  8. 


mi.        rd.      yd. 

120    90    0 

ft.      in. 

2     7 
5 

601  130    4 

0  11 

COMPOUND  NUMBERS.  283 

4.  18  cu.  yd.  16  cu.  ft.  9  cu.  in.  by  7. 

5.  16  sq.  yd.  7  sq.  ft.  86  sq.  in.  by  5. 

6.  9  yr.  7  mo.  15  d.  by  6. 

7.  How  much  wheat  in  a  load  of  18  sacks,  each 
containing  3  bu.  1  pk.  ? 

8.  What  is  the  area  of   3  pieces  of  land,  each, 
containing  36  A.  120  sq.  rd.  ? 

9.  Henry  is  9  yr.  6  mo.  15  d.  old.     This  is  one- 
fourth  of  his  father's  age  ;  how  old  is  his  father  ? 

DIVISION    OF    COMPOUND    NUMBERS. 

26.    Divide  21  w.  5  d.  14  h.  9  min.  by  6. 

£  of  21  weeks  is  3  weeks  and  3 

weeks    remaining.      3  w.  =  21  d- 

21d.  +  5d.  =  26d.    £of26d.=4d. 

and  2  d.  remaining.     2  d.  =  48  h. 

£  of  62  h.  =  10  h.  and  2  h.  remain- 

120  min.  +  9  min#=  129  min.     £  of 

11%  min. 

Divide : 

1.  50  bu.  3  pk.  7  qt.  by  6. 

2.  25  gal.  3  qt.  1  pt.  by  5. 

3.  14  cwt.  60  lb.  8  oz.  by  8. 

4.  18  h.  25  min.  28  sec.  by  4. 

5.  20  cu.  yd.  20  cu.  ft.  9  cu.  in.  by  7. 

6.  28  sq.  yd.  7  sq.  ft.  120  sq.  in.  by  9. 

7.  If  a  man  dig  a  ditch  34  rd.  3  yd.  2  ft.  long 
in  6  days,  what  length  can  he  dig  in  1  day  ? 


w. 

d. 

h. 

min. 

6 

)21 

5 

14 

9 

3 

4 

10 

21£ 

48  h 

.  +  14  h 

.  =  i 

32  h. 

ing. 

2h. 

= 

120 

min. 

129: 

min.  : 

=  2 

li  min. 

284  ELEMENTARY  ARITHMETIC. 

8.  How  many  bottles,  each  holding  2  qt.  1  pt., 
can  be  filled  from  a  can  holding  7  gal.  3  qt.  of 
varnish  ? 

Note.  —  Reduce  both  compound  numbers  to  the  same 
denomination,  pints,  and  divide  as  in  simple  numbers. 

9.  How  many  sacks,  each  holding  2\  bushels, 
can  be  filled  from  a  bin  containing  35  bu.  3  pk.  ? 

27.     MISCELLANEOUS    PROBLEMS. 

1.    How  many  square  inches  in  a  rectangular 

surface  which  is  9  inches  by  12  inches? 

2.    How     many     square 

inches  in  a  triangular  pane 

of  glass  whose  base  is  12 

inches    and    whose    height 

is  9  inches  ? 

The  area  of  a  triangle  is  one- 
half  the  area  of  a  rectangle 
with  the  same  base  and  altitude  (height).  Consider  one 
side  of  the  triangle  as  the  base ;  measure  from  the  base  to 
the  angle  opposite  for  the  altitude.  The  pane  of  glass  con- 
tains -J  of  108  inches,  which  is  54  inches.  4J-  inches  (one-half 
of  altitude)  multiplied  by  12  inches  (base)  equals  54  inches, 
area  of  the  triangle. 

To  find  the  area  of  a  triangle  : 
Multiply  the  base  by  half  the  altitude, 

3.  How  many  square  feet  in  the  gable  of  a  house 
if  the  base  is  25  feet  and  the  altitude  12|  feet  ? 

4.  How  many  square  rods  in  a  triangular  field 
whose  base  is  20  rods  and  altitude  14  rods  ? 


MISCELLANEOUS   PROBLEMS. 


285 


5.  Find  the  number  of 
acres  in  a  farm  from  the 
diagram. 

First,  find  the  area  of  the 
square.*  then  the  area  of  the 
triangle. 


6.  Find    from    the    dia-    (c 
gram  the  number  of  square 
yards  of  tiling  used  for  the 
floor  of  a  corridor. 

Divide  into  two  rectangles  and 
find  the  area  of  each. 

7.  Find  the  number  of 
square  yards  in  the  floor  of 
this  room. 

Divide  into  two  rectangles,  one 
of  which  shall  be  2  feet  by  6  feet. 

8.  How  many  square  yards  in  the  ceiling  ? 

9.  How  many  square  yards  in  the  walls  of  a 
room  20  feet  by  16  feet,  and  9J  feet  high,  if  no 
allowance  is  made  for  doors  and  windows  ? 

The  area  of  the  four  walls  of  a  room  is  equal  to  that  of  a 
rectangle  whose  length  is  equal  to  the  sum  of  the  four 
sides,  and  whose  breadth  is  equal  to  the  height  of  the  room. 

2  x  20  ft,  +  2  x  16  ft.  =  72  ft.  72  ft.  x  9£  ft.  =  684  sq.  ft. 
684  sq.  ft.  -f-  9  =  76  sq.  yd. 

Draw  the  rectangle  which  represents  the  area  of  the 
walls  of  the  room. 


236  ELEMENTARY  ARITHMETIC. 

30  ft. 


10.    How    many    square 
S    yards    in    walls,    floor,    and 
ceiling  of  this  room  ? 


11.  How  many  square  yards  in  a  roof  the  raf- 
ters of  which  are  16  feet  long  and  the  ridge-pole 
25  feet  long. 

12.  If  the  height  of  a  staircase  is  15  feet,  and 
that  of  each  step  is  9  inches,  how  many  steps  are 
there  in  the  staircase  ? 

13.  How  many  yards  of  carpet,  f  of  a  yard  wide, 
will  be  required  to  carpet  a  floor  20  feet  by  19  feet  ? 

We  must  decide  whether  the  strips  are  to  run  across  the 
room  or  lengthwise,  and  how  much  must  be  turned  under  or 
cut  off.  The  number  of  yards  in  a  strip  multiplied  by  the 
number  of  strips  will  give  the  required  number  of  yards. 

In  this  case  we  decide  to  lay  the  strips  across  the  room ; 
20  feet  divided  by  J  of  a  yard  will  give  the  number  of  strips. 

|  of  a  yard  equals  2\  feet.  20  feet  divided  by  2\  feet 
equals  8§  (times).  8§  is  the  number  of  strips  required. 
We  must  buy  9  strips,  and  turn  under  or  cut  off  ^  of  the 
width  of  one  strip.  19  feet  equals  6 J  yards,  the  length  of 
each  strip  if  we  cut  the  strips  the  exact  length  of  the  room. 
But  if  we  allow  J  of  a  yard  for  turning  under,  the  strips 
will  be  6§  yards  in  length.  6f  yards  X  9  =  60  yards,  the 
number  of  yards  required. 

14.  How  many  yards  of  carpet,  f  of  a  yard  wide 
will  be  required  for  a  floor  24  feet  by  151  feet,  if 
the  strips  run  crosswise  ? 


MISCELLANEOUS  PROBLEMS.  287 

15.  How  many  yards  of  carpet,  I  of  a  yard  wide, 
will  be  required  for  a  room  1\  yards  long,  6  yards 
wide,  if  the  strips  run  lengthwise  and  there  is  a 
waste  of  I  of  a  yard  in  each  strip  in  matching  the 
pattern  ? 

16.  How  many  yards  of  carpet  will  be  required 
for  a  stair  of  12  steps,  if  each  step  is  18  inches 
wide  and  1\  inches  high  ? 

17.  How  many  cords  of  wood  in  a  pile  40  feet 
long,  4  feet  wide,  and  5^  feet  high  ? 

18.  How  many  cords  of  wood  can  be  piled  under 
a  shed  24  feet  long,  18  feet  wide,  and  12  feet  high  ? 

19.  How  many  boxes,  4  inches  long,  3  inches 
wids,  and  2  inches  deep,  can  be  packed  in  a  box  3 
feet  long,  3  feet  wide,  and  2  feet  deep,  measured 
on  the  inside  ? 

20.  How  many  fence  boards,  each  16  feet  long, 
will  be  required  to  fence  a  field  80  rods  long  and 
40  rods  wide,  the  fence  being  4  boards  high  ? 

21.  Mr.  A.'s  orchard  covers  2|  acres.  Allowing 
two  square  rods  for  each  tree,  how  many  trees  are 
there  ? 

22.  How  many  loads  of  earth  of  1  cubic  yard 
each  will  be  needed  to  fill  in  a  lot,  45  feet  front, 
90  feet  deep,  to  raise  it  1|  feet? 


CHAPTER  VII. 


PERCENTAGE. 

1.  1.  A  man  gave  away  6  dollars  out  of,  every 
hundred  dollars  he  had.  How  many  dollars  did 
he  give  out  of  200  dollars?  Of  300  dollars? 
Of  600? 

2.  7  is  what  part  of  100  ?  9  is  what  part  of 
100?     1  is  what  part  of  100? 

One  one-hundredth  of  a  number  is  one  per  cent 
of  it ;   two  hundredths,  two  per  cent. 
The  term  per  cent  means  by  the  hundred. 

Any  per  cent  of  a  number  is  so  many  hundredths 
of  it.     The  rate  per  cent  is  the  rate  per  hundred. 

3.  6  hundredths  of  a  number  is  what  per  cent 
of  it  ?     4  hundredths  ?     10  hundredths  ? 

4.  What  per  cent  of  a  number  is  m  of  it?  ^? 

2^.e>     68?  1Q0  9  150  9 

100  *  100  •     100  •     100  • 


PERCENTAGE.  289 

5.  What  per  cent  of  a  number  is  .05  of  it  ?  .15 
of  it  ?  .45  ?  .121  ?  .661  ?  .03^  ? 

The  character  %,  called  the  per  cent  sign,  is 
used  for  the  words  per  cent.  8  %  is  read,  8  per 
cent,     s  %  is  read,  1  of  1  per  cent. 

6.  How  many  hundredths  of  a  number  is  6  %  of 
it  ?  9  %  of  it  ?  10  %  ?  71  %  ?  50  %  ?  150  %  ? 

2.  Any  per  cent  of  a  number  may  be  expressed 
in  four  wTays :  In  words,  as  a  common  fraction,  as 
a  decimal  fraction,  and  by  the  per  cent  sign. 

1.  Express  decimally:  6  %,  11%,  125%,  150%. 

125  %  =  1.25 

2.  Express  decimally:  121%,  181%,  171  %,  33|%, 

871%,  1121%. 

18|  %  rs  .18f 

3.  Express,  first  as  a  common  fraction,  then  as 

a  decimal :  3  %,  5  %,  8  %,  121  %  ,  |  of  1,  f  of  1  per 

cent,  |  of  1,  |  of  1  per  cent,  1  per  cent,  3  per  cent, 

|  of  1  per  cent. 

First,  !  of  1  %  —  %  of  TJ0  =  ,{fo;  second,  f  %  expressed 
decimally  =  .00f .    Arts. 

!  %  is  how  many  ten-thousandths,  expressed  decimally. 

Write  and  complete  the  following  table  : 

£  =  .50  =  50  %  |  =  .75  =  75  %  f  =  ?  £  =  ? 

£  =  .33£  =  33J%  £  =  .20  =  20%  £  =  ?  |  =  ? 

§  =  .66§  =  66§%  |  =  .40  =  40%  |  =  ?  #  =  ? 

i  =  .25  =  25  %  f  =  .60  =  60  %  f  =  ?  £  =  ? 

19E 


290  ELEMENTARY  ARITHMETIC. 

3.     To  find  a  given  per  cent  of  any  number. 

(      1.    What  is  5  %  of  300  ? 

5  %  of  300  is  Tfo  of  300.    Tfo  of  300  =  3.     Tfo  of  300  =  15. 
5  %  of  300  is  15.     Expressed  decimally,  300  x  .05  =  15. 

2.  What  is  4  %  of  600  ?  800  ?  900  ?  250  ? 

3.  What  is  8  %  of  200  ?  300  ?  480  ?  560  ? 
Express  the  rates  decimally. 

4.  What  is  7  %  of  350  ?  9  %  of  630  ?   10  %  of 
900? 

5.  What  is  8|  %  of  $984.36  ?     (8J  %  =  .081.) 

6.  What  is  6  %  of  $650.80  ?     121  %  of  $500  ? 

7.  What  is  3|  %  of  360  days  ? 

8.  What  is  110  %  of  250  bushels? 

9.  What  is  200  %  of  250  bushels  ? 

10.  What  is  \  %  of  $60.50  ?    \  %  of  $45  ? 

11.  I  bought  a  lot  for  $500,  and  sold  it  for  8  % 
more  than  it  cost  me;  what  was  my  gain  ? 

12.  If  a  lot  is  bought  for  $500,  and  sold  for  6  % 
less  than  the  cost,  what  is  the  loss  ? 

13.  In  a  school  of  200  pupils  6  °fo  are  absent ; 
how  many  are  absent  ?     How  many  are  present  ? 

14.  A  man  having  400  acres  of  land  gave  25  °fo 
of  it  to  his  son ;  how  many  acres  did  he  give  away  ? 


PERCENTAGE.  291 

4:.     To  find  what  per  cent  one  number  is  of  another. 

1.  4  is  what  per  cent  of  16  ? 

The  first  step  in  such  problems  is  to  find  what  part  one 
number  is  of  another.     4  is  what  part  of  16  ? 

1  is  TV  of  16.     4  is  T\  or  \  of  16.     \  =  fifa  =  25  %. 
Expressed  decimally,  16  )  4.00  (  .25 
32 
80 
80 

2.  What  per  cent  of  12  is  4  ?  Of  60  is  12  ?  Of 
56  is  8  ? 

3.  8  is  what  per  cent  of  72  ?  15  of  45  ? 

4.  What  per  cent  of  90  cents  is  15  cents  ?  12| 
cents  is  what  per  cent  of  75  cents  ? 

5.  What  per  cent  of  $640  is  $48  ? 

6.  $27  is  what  per  cent  of  $600?  $5.10  of  $85? 
$17  of  $85?    50  cents  of  $2? 

7.  1  mile  is  what  per  cent  of  2  miles  ?  61  bush- 
els of  25  bushels  ? 

8.  A  boy  bought  oranges  at  3  cents  apiece,  and 
sold  them  at  4  cents  apiece.  Compare  the  gain 
with  the  cost.  What  per  cent  did  he  make  on 
the  cost  ? 

9.  A  merchant  bought  silk  at  $3  a  yard,  and 
sold  it  at  $4  a  yard.  Compare  the  cost  with  the 
selling  price  ;  the  cost  is  what  per  cent  of  the 
selling  price  ? 


292  ELEMENTARY  ARITHMETIC. 

10.  A  rug  which  cost  $3  is  sold  for  $4.  The 
selling  price  is  what  per  cent  of  the  cost  ? 

Note.    The  selling  price  is  the  cost  plus  what  per  cent  of  the  cost  ? 

5.    To  find  a  number  when  a  per  cent  of  it  is  given. 

1.  30  is  6  %  of  what  number  ? 

1  %  of  the  number  is  J  of  30,  which  is  5.  The  number 
required,  or  100  %,  is  100  times  5,  which  is  500.  30  is  6  % 
of  500.  The  same  result  is  obtained  by  dividing  the  given 
number  by  the  rate  per  cent  expressed  decimally. 

(V-  X  100)  =  (30  -h  .06) 

2.  80  is  10  %  of  what  number  ?     40  ?     60  ? 

3.  60  is  30  °Io  of  what  number  ?     90  ?     120  ? 

4.  100  is  50  %  of  what  number  ?     80  ?     200  ? 

5.  80  is  100  %  of  what  number  ?     200  ?     50  ? 

6.  150  is  150  %  of  what  number  ?     15  ?     25  ? 

7.  80  is  121  %  of  what  number  ? 

Express  decimally,  .125  )  80.000  (  640.   Arts. 
75  0 
5  00 
5  00 

Find  the  number  of  which  : 

8.  $75.52  is  8%.       11.    $3.35  is  331%. 

9.  $810  is  90  %.       12.    300  bushels  is  150  %. 
10.    $30  is  2  %.  13.    300  acres  is  200  %. 
14.    A  house  rents  for  $180,  which  is  6  %  of  its 

•value  ;  what  is  its  value  ? 


INTEREST.  29a 

15.  An  etching  cost  $48,  which  is  80  %  of  the 
cost  of  an  engraving;  what  is  the  cost  of  an 
engraving  ? 

16.  The  width  of  a  table  is  4  feet,  which  is  80  °fo 
of  the  length.     What  is  the  length  of  the  table  ? 

17.  If  the  length  of  a  table  is  5  feet,  and  this  is 
125  %  of  the  width,  how  wide  is  the  table  ? 

18.  The  width  of  a  field  is  40  rods,  which  is 
25  %  of  the  length.     How  long  is  the  field  ? 

6.   INTEREST. 

1.  If  I  borrow  $100,  and  pay  $6  for  the  use 
Of  it  for  a  year,  what  per  cent  of  the  $100  do 
I  pay? 

2.  If  I  had  paid  6  %  of  the  $100,  how  much 
money  would  I  have  paid  ?     5  %  ?     7  %  ?     8  %  ? 

Money  paid  for  the  use  of  money  is  called  In- 
terest. It  is  reckoned  at  a  given  rate  per  cent 
by  the  year. 

The  money  on  ivhich  the  interest  is  paid  is  called 
the  Principal. 

The  sum  of  principal  and  interest  is  called  the 
Amount. 

3.  What  is  the  interest  of  $200  for  one  year 
at  6  %  ?     For  2  years  ? 


294  ELEMENTARY  ARITHMETIC. 

What  is  the  interest  on  : 

4.  $200  for  1  year  at  5  °fo  ? 

5.  $300  for  2  years  at  5  %  ? 

6.  $400  for  3  years  at  5  %  ? 

7.  $200  for  2}  years  at  6  %  ? 

8.  $100  for  6  months  at  6  %  ? 

9.  $300  for  1  yr.  6  mo.  at  4  %  ? 

7.    1.   What  is  the  interest  on  $320  for  2  yr. 

8  mo.  and  26  d.  at  8  %  ? 

$320  2  yr.  8  mo.  =  32  mo. 


.08 


$2,133  int.  for  1  mo. 


12 )  $25.60  int.  for  1  y r.  32 

30)  2.133  int.  fori  mo.  ~4266 

.0711  int.  for  Id.  6399 

^  $687256  int.  for  2  yr.  8  mo. 

4266  _A8^  int-  for  26  d- 

1422  $70,104  int.  for  2  yr.  8  mo.  26 d. 
$1.8486  int.  for  26d. 

What  is  the  interest  on  : 

2.  $450  for  1  yr.  9  mo.  12  d.  at  6  %  ?     At  7  %  ? 

3.  $600  for  2  yr.  3  mo.  16  d.  at  5  %  ?     At  8  %  ? 

4.  $80.75  for  2  yr.  6  mo.  12  d.  at  6  %.     At 
4%? 

5.  Find  the  amount  of  $190.80  for  2  yr.  9  mo. 
at  6  %. 

6.  Find  the  amount  of   $200  for  5  yr.  4  mo. 
20  d.  at  4  %. 


REVIEW.  295 

Find  the  amount : 

7.  $650,  from  Oct.  4,  1884,  to  May  6,  1886, 
at  6  %. 

8.  $1200,  from  Nov.  15,  1884,  to  March  1, 1887, 
at  5  °lo. 

8.      ORAL  REVIEW. 

1.  6  is  50  %  of  what  number  ?  6  is  50  %  more 
than  what  number?     6  is  150  %  of  what  number? 

2.  8  is  200%  of  what  number?  8  is  100% 
more  than  what  number? 

3.  9  is  25  %  of  what  number  ?  9  is  25  %  less 
than  what? 

4.  Sold  a  lamp  for  $6,  and  gained  $1 ;  what 
per  cent  did  I  gain  ? 

5.  If  a  lamp  is  bought  for  $5,  and  sold  at  20  % 
profit ;  what  is  the  selling  price  ? 

6.  If  chestnuts  are  bought  at  8  cents  a  quart 
and  sold  at  12  cents,  what  is  the  gain  per  cent  ? 

7.  In  a  school  of  60  pupils,  80  %  entered  on  the 
first  day  of  the  term ;  how  many  have  entered  the 
school  since  ? 

8.  If  pineapples  are  sold  at  15  cents  each,  and 
this  is  25  %  more  than  the  cost,  what  was  the 
cost? 

9.  If  pineapples  are  bought  for  12  cents  each, 
and  sold  for  16  cents,  what  per  cent  is  gained  ? 


296  ELEMENTARY  ARITHMETIC. 

10.  Henry  is  4  feet,  5  inches  tall,  and  his 
brother  is  20  %  taller ;  how  many  feet  tall  is  his 
brother  ? 

11.  A  boy  bought  cherries  at  125  cents  a  quart, 
and  sold  them  at  200  %  on  the  cost ;  for  what  did 
he  sell  them  ? 

12.  A  number  which  is  25  %  less  than  12  is 
what  per  cent  of  12  ? 

13.  5  pounds  of  soap  lost  4  ounces  by  drying ; 
what  per  cent  of  the  original  weight  was  water? 

14.  Cloth  which  cost  $1.25  a  yard  was  sold  for 
$1.37|;  what  was  the  gain  per  cent  ? 

15.  For  what  must  cloth  which  cost  $1.25  a 
yard  be  sold  to  gain  10  %  ? 

16.  If  I  sell  cloth  for  $1.50  a  yard,  at  a  gain  of 
121  cents  a  yard,  what  per  cent  do  I  gain  ? 

17.  $8  is  50  %  less  than  the  cost  of  a  coat; 
what  is  the  cost? 

18.  A  man  sold  a  horse  for  $120,  and  thereby 
gained  \  of  the  cost ;  what  per  cent  did  he  gain  ? 
$120  is  how  many  fifths  of  the  cost  ? 

19.  From  a  hogshead  containing  63  gallons  of 
molasses  12  gallons  leaked  out.  What  per  cent 
of  the  whole  was  the  leakage  ? 

20.  What  number  diminished  by  50  °fo  of  itself 
equals  15  ?     200  ?     150  ? 


REVIEW.  297 

21.  What  number  increased  by  50  °fo  of  itself 
equals  15?     150?     300? 

22.  15  is  how  many  times  10  ?  15  is  what  per 
cent  of  10  ? 

23.  A  barrel  of  flour  sells  for  $8.40  at  a  profit 
of  20  %  ;  what  was  the  cost  ? 

24.  After  30  %  of  a  mast  had  been  broken  off 
by  the  wind,  it  was  105  feet  high  ;  what  was  the 
height  at  first  ? 

25.  The  length  of  a  shadow  cast  by  a  tree  is 
28  °fo  longer  than  the  height  of  the  tree.  If  the 
tree  is  72  feet  high,  how  long  is  the  shadow  ? 

26.  If  $12  at  interest  for  3  years  gains  $2.16, 
what  will  be  the  interest  for  one  year?  On  $1 
for  one  year. 

27.  If  $6  gain  $1.08  in  3  years,  how  much  will 
$1  gain  in  one  year  ? 

28.  If  $1  gains  9  cents  in  a  year,  how  long  will 
it  take  it  to  gain  72  cents  ?  How  long  will  it  take 
$4,  at  the  same  rate,  to  gain  the  same  amount  ? 

29.  If  $1  gains  5  cents  in  a  year,  how  long  will 
it  take  $6  to  gain  90  cents  ? 

30.  If  $1  earns  6  cents  in  a  }^ear,  how  many 
dollars  will  earn  $1.80  in  3  years  ? 


298  ELEMENTARY  ARITHMETIC. 


CHAPTER    VIII. 
MISCELLANEOUS    PROBLEMS. 

Note.  The  following  problems  do  not  constitute  a  necessary  part  of 
an  elementary  course  in  arithmetic.  They  are  added  here  because  of 
their  value  for  review  work,  or  for  use  by  pupils  who  may  be  somewhat 
in  advance  of  the  class. 

CANCELLATION. 

1.  How  many  bushels  in  8  boxes  of  beans,  each 
containing  20  quarts  ? 

2.  The  factors  of  a  dividend  are  16,  50,  and 
.9 ;  of  the  divisor,  .15,  8,  and  2.  'What  is  the 
quotient  ?     Divide  56  x  14.4  by  14. 

3.  A  farmer  gave  55  sheep  for  11  young  horses 
worth  $60  each.  What  money  value  did  he  get 
for  each  sheep  ?     f  of  n  of  £  =  ? 

4.  How  many  barrels  of  36  gallons  each  will  con- 
tain as  much  as  12  hogsheads  of  63  gallons  each? 

5.  If  1  man  can  mow  6  acres  of  grass  in  a  day, 
how  many  men  will  it  take  to  mow  3  fields  of  56 
acres  each  ? 

6.  At  60  cents  a  cord,  how  many  days  will  it 
take  a  man  to  earn  $75.00,  if  he  saws  2  cords  of 
wood  a  day? 

7.  If  a  turkey  weighing  101  pounds  cost  $1.68, 
what  will  be  the  cost  of  one  that  weighs  15f  pounds? 


MISCELLANEOUS  PROBLEMS.  299 

<       COMMON  FRACTIONS. 

1.  At  |  of  a  dollar  per  yard,  how  many  yards 
of  cloth  can  be  bought  for  §  of  a  dollar  ? 

2.  At  the  rate  of  2\  dollars  for  3  baskets  of 
peaches,  what  is  that  per  basket  ? 

3.  If  I  use  1  of  a  pound  of  sugar  in  making  one 
cake,  how  many  cakes  can  I  make  with  2\  pounds  ? 

4.  Helen  divided  If  pounds  of  nuts  equally 
among  5  playmates.  What  part  of  a  pound  did 
each  receive  ? 

5.  Horace  divided  5  apples  equally  among  6 
boys.     What  part  of  one  apple  did  each  receive  ? 

6.  At  \\  dollars  each,  how  many  lamps  can  be 
bought  for  6|  dollars  ? 

7.  A  man  divided  8|  dollars  among  his  chil- 
dren, giving  them  1|  dollars  apiece.  How  many 
children  had  he  ? 

8.  At  2|  dollars  a  box,  how  many  boxes  of 
lemons  can  be  bought  for  6|  dollars? 

9.  At  &  of  a  dollar  per  yard,  how  many  yards 
of  ribbon  can  be  bought  for  2f  dollars  ? 

10.  A  gentleman  gave  away  \  of  the  books  in 
his  library,  lent  \  of  the  remainder,  and  sold  \  of 
what  was  left.  He  then  had  360  books  remain- 
ing.    How  many  had  he  at  first  ? 

11.  If  a  lady  spends  4|  dollars  per  month  for 
car  fare,  in  what  time  will  she  spend  $271? 


300  ELEMENTARY  ARITHMETIC. 

DECIMAL  FRACTIONS. 

1.  The  owner  of  a  schooner  sells  .35|  of  the  ves- 
sel to  the  captain.     What  part  does  he  still- own  ? 

2.  The  minuend  is  67.081.  What  must  the 
subtrahend  be  to  leave  a  remainder  of  56.009  ? 

3.  The  less  of  two  numbers  is  3207.56  and  their 
difference  is  978.756.     Find  the  greater  number. 

4.  A.  owns  Kj  of  an  iron  foundry  and  sells  .75 
of  his  share  for  $2100.  What  is  the  value  of  the 
whole  foundry  ? 

5.  What  is  the  gain  on  5000  bushels  of  wheat, 
bought  in  Chicago  at  $1.4375  per  bushel  and  sold 
in  New  York  at  $1,625  per  bushel,  allowing  15 
cents  per  bushel  for  transportation? 

6.  A  flour  merchant  bought  137  barrels  of  flour 
at  $7,875  per  barrel.  He  sold  89  barrels  at  $9,378 
per  barrel,  and  the  remainder  brought  only  $5.80 
per  barrel.     What  was  his  gain  ? 

7.  Two  men  start  from  the  same  place  and  travel 
in  opposite  directions.  One  travels  119.33  miles 
a  day,  and  the  other  123.75  miles  a  day.  How  far 
will  they  be  apart  at  the  end  of  six  days  ? 

8.  I  sold  .36  of  my  land  for  $900.  How 
much  is  the  remainder  of  it  worth  at  the   same 

rate  ? 

9.  Divide  $3679.94  by  $5,004. 

10.    Divide  6504.5  yards  by  5.06  yards. 


MISCELLANEOUS  PROBLEMS.  301 

MENSURATION. 

1.  Supposing  each  child  in  a  schoolroom  ought 
to  have  80  cubic  feet  of  air,  how  many  children 
should  sit  in  a  room  which  is  20  feet  long,  18  feet 
wide,  and  12  feet  high  ? 

2.  How  many  tiles,  each  3  inches  square,  will 
cover  the  space  around  a  fireplace  5  feet  long  and 
3  feet  wide  ? 

3.  The  walk  from  our  kitchen  door  to  the  stable 
is  75  feet  long  and  4.5  feet  wide.  How  many 
bricks  in  it,  each  brick  being  8  inches  by  4  inches  ? 

4.  How  many  times  is  4  cubic  inches  contained 
in  a  four-inch  cube  ? 

5.  How  many  cubic  inch  blocks  will  a  box  con- 
tain which  is  1  ft.  long,  |  ft.  deep,  and  8  in.  wide  ? 

,     6.    How  many  gallons  will  fill  a  tank  8|  feet  by 
6|  feet  by  5  feet  ?     (231  cubic  inches  in  a  gallon.) 

7.  How  many  loads  of 
earth  must  be  removed 
in  digging  a  cellar  of 
the  dimensions  given  in 
the  diagram. 

(A  cubic  yard  is  understood  to  be  a  load.) 

Papering  and  Plastering, 
1.    How  many  square  yards  of  plastering  in  the  4 
walls  of  a  room  14  ft.  long,  12|  ft.  wide,  and  8  ft. 
high,  if  no  allowance  is  made  for  doors  and  windows  ? 


40  ft. 

8  ft. 

deep. 

load.) 

t 

302  ELEMENTARY  ARITHMETIC. 

2.  How  many  square  yards  of  plastering  in  the 
ceiling  of  a  room  15§  feet  long  by  14  feet  wide? 
If  this  room  is  9  feet  high  above  the  baseboard, 
how  many  square  yards  in  the  walls  and  ceiling 
together,  no  allowance  for  doors  and  windows  ? 

3.  How  many  square  yards  of  plastering  in  the 
walls  and  ceiling  of  a  room  16  feet  long,  14|  feet 
wide,  and  9  feet  high,  if  14  square  yards  be  al- 
lowed for  doors,  windows,  and  baseboard? 

4.  How  many  rolls  of  paper  18  in.  wide  will  be 
required  to  paper  the  walls  of  a  room  20  ft.  long, 
19  ft.  wide,  and  9  ft.  high,  deducting  60  sq.  ft.  for 
the  surface  of  one  door  and  two  windows,  and 
allowing  \  a  roll  for  waste  in  matching? 

(The  height  is  measured  from  the  top  of  the  baseboard.) 

Note  1.  The  cheapest  wall  paper  is  18  in.  wide.  In  American  paper, 
the  single  rolls  are  8  yd.  long;  the  double  rolls  are  16  yd.  long.  A  single 
roll  is  understood  unless  a  double  roll  is  given  in  the  problem.  There  are 
36  sq.  ft.  of  covering  surface  in  a  single  roll  of  18  in.  paper  (24  ft.  X  1^  ft. 
=  36sq.  ft.). 

Note  2.  The  walls  of  a  room  20  ft.  by  19  ft.  and  9  ft.  high,  make  a 
rectangle  78  ft.  long  by  9  ft.  wide,  which  contains  702  sq.  ft.  Deducting 
60  sq.  ft.  for  doors  and  windows  (20  sq.  ft.  for  each),  there  are  642  sq.  ft. 
642  sq.  ft.  -f  36  sq.  ft.  =  17|.  Adding  \  a  roll  for  waste,  184,  rolls  is  the 
amount  required. 

5.  How  many  rolls  of  paper  30  in.  wide  will  be 
required  to  paper  the  walls  and  ceiling  of  a  room 
30  ft.  long,  26  ft.  wide,  and  10  ft.  high,  allowing 
120  sq.  ft.  for  doors  and  windows,  and  §  of  a  roll 
for  waste  ? 

(How  many  square  feet  of  surface  in  a  single  roll  of  30  in.  paper  ?) 


MISCELLANEOUS  PROBLEMS.  303 

BOARD  MEASURE. 

Note  1.  Board  measure  is  a  kind  of  surface  measure,  and  is  employed 
in  measuring  lumber.  The  unit  of  lumber  measurement  is  a  board  foot, 
which  is  1  foot  long,  1  foot  wide,  and  1  inch  thick.  Lumber  1  inch  or  less 
m  thickness  is  considered  inch-lumber. 

1.  How  many  feet  of  lumber  in  a  board  15  feet 
long,  9  inches  wide,  and  1  inch  thick  ? 

Note  2.  When  a  board  is  12  feet  long,  every  inch  in  width  is  equivalent 
to  a  board  foot.  This  board  is  1 5  feet  long  and  every  inch  in  width  is 
equivalent  to  l£  board  feet.    15  -=-  12  =  lj.     l£  X  9  =  ll£  (board  feet). 

To  find  the  number  of  feet  of  lumber  in  a  board  1  inch  or  less  in 
thickness : 

Multiply  the  length  in  feet  by  the  width  in  inches 
and  divide  the  product  by  12, 

2.  How  many  feet  of  lumber  in  a  board  20  feet 
long  and  10  inches  wide  ?  How  many  in  a  board 
16  feet  long  and  7  inches  wide  ? 

3.  How  many  feet  of  lumber  in  a  plank  15  feet 
long,  18  inches  wide,  and  3  inches  thick  ? 

Note  3.  The  measurement  of  this  plank  is  equal  to  the  measurement 
of  three  inch-boards  of  the  same  length  and  width. 

4.  How  many  feet  of  lumber  in  a  plank  18  feet 
long,  9  inches  wide,  and  11  inches  thick  ? 

(Every  sq.  ft.  of  this  plank  is  equal  to  l£  board  feet.) 

5.  How  many  feet  of  lumber  in  a  pile  of  twenty 
boards  16  feet  long,  10  inches  wide,  and  1  an  inch 
thick?     (See  note  1  above.) 

6.  How  many  feet  of  lumber  in  a  board  14  feet 
long,  9  inches  wide  at  one  end,  and  5  inches  wide 
at  the  other,  tapering  uniformly  ? 


304  ELEMENTARY  ARITHMETIC. 

PERCENTAGE. 

1.  A  grocer  sold  apples  at  $1  a  bushel,  which 
was  125%  of  their  cost.     Find  the  cost  per  bushel  ? 

2.  By  selling  a  knife  for  75  cents  a  boy  gains 
25%  on  the  cost.     What  was  the  cost  of  the  knife? 

(Hint :  75  cents  is  what  per  cent  of  the  cost  ?) 

3.  By  selling  a  book  for  75  cents  I  lost  25%  on 
the  cost.     What  was  the  cost  of  the  book  ? 

4.  Henry  sold  a  pair  of  skates  for  90  cents, 
thereby  losing  40%  of  the  cost.  What  did  he  pay 
for  the  skates? 

5.  A  boy  received  a  half-peck  of  cherries  for 
every  bushel  he  picked.  What  per  cent  did  he 
receive  ? 

6.  Henry  had  $1.80  and  spent  72  cents  for  a 
box  of  water  colors.  What  per  cent  of  his  money 
did  he  spend? 

7.  A-  man  sold  a  horse  for  $120  and  thereby 
gained  \  of  the  cost.     What  per  cent  did  he  gain  ? 

8.  A  horse  was  bought  for  $160  and  sold  for 
$120.     What  was  the  loss  per  cent? 

9.  A  box  of  slippers  containing  one  dozen  pairs 
cost  $21.  I  wish  to  sell  them  so  as  to  gain  33s%. 
For  what  price  must  I  sell  each  pair  ? 

10.  Out  of  30  bushels  of  potatoes,  2^  bushels 
were  unfit  for  use.  What  per  cent  of  them  were 
sound  ? 


MISCELLANEOUS  PROBLEMS.  305 

11.  James  buys  a  knife  for  50  cents  and  sells 
it  to  Fred  for  60  cents;  what  per  cent  does  he 
gain?  Fred  sells  the  knife  to  Tom  for  50  cents; 
what  per  cent  does  he  lose  ?  Can  you  explain  the 
difference  in  these  rates  ? 

12.  A  man  owing  $500  agrees  to  pay  the  debt 
in  instalments,  the  first  to  be  50  %  of  the  whole, 
the  second  25  %,  the  third  15  %,  the  fourth  10  %  ; 
what  will  be  the  amount  of  each  payment  ? 

Note.  Dealers  buy  many  kinds  of  goods  at  less  than  list  prices,  such 
allowance,  when  made,  being  reckoned  at  an  agreed  per  cent  of  list  price. 
This  allowance  is  called  trade  discount. 

13.  The  Bowen-Merrill  Company  ordered  books 
which  at  list  amounted  to  $150.  The  discount 
allowed  was  16§  %.  What  was  the  amount  of  the 
bill? 

14.  If  the  books  purchased  in  the  last  example 
are  sold  at  list,  or  for  a  total  of  $150,  what  is  the 
gain  per  cent  on  the  purchase  price  ? 

15.  Find  the  gain  per  cent  on  the  purchase 
price  if  the  above  books  are  sold  at  10  %  advance 
on  list  prices.     At  20  %.     At  25  %. 

16.  Ten  sets  of  wall  maps  listed  at  $25  per  set 
were  sold  to  a  school  board  at  25  %  discount.  The 
party  selling  them  purchased  the  maps  from  the 
manufacturer  at  50  %  discount  from  the  list  price. 
What  per  cent  profit  did  he  make  on  the  purchase 
price  ? 

20E 


306  ELEMENTARY  ARITHMETIC. 

INTEREST. 

1.  Mrs.  Dewey  has  24  government  bonds  of 
$1000  each,  bearing  4  %  interest.  What  is  her 
annual  income  from  these  bonds  ? 

2.  A  borrowed  $360  of  his  neighbor,  agreeing 
to  pay  him  interest  at  the  rate  of  7  %  per  annum. 
At  the  end  of  2\  years  A  paid  the  principal  and 
interest.     What  was  the  amount  paid? 

3.  Mr.  Simmons  sold  his  saddle  horse  to  Dr. 
Jordan  for  $150,  receiving  cash  $60,  and  a  note 
for  the  remainder  bearing  6  %  interest,  due  1  year 
and  9  months  from  date.     What  was  due  on  this 

note  when  it  matured  ? 

i 

4.  Henry  Nelson  worked  7  months  for  Nickel 
&  Co.  at  $60  per  month,  drawing  \  of  his  salary 
each  month.  At  the  end  6i  the  7  months  he  re- 
ceived cash  for  one-half  the  amount  then  due  him, 
and  a  note  for  the  remainder  due  in  9  months  at 
8  °/0  interest.  What  was  the  amount  of  the  note 
at  maturity  ? 

5.  Mr.  Jones  owes  an  account  amounting  to  $60, 
which  is  past  due  4  months.  He  agrees  to  give  his 
note  due  1  year  from  date  at  7  %  interest  for  the 
amount  of  the  account  plus  the  interest  at  6%  for 
the  4  months  it  has  been  overdue.  What  will  be 
the  face  of  the  note,  and  what  the  amount  at  its 
maturity  ? 


MISCELLANEOUS  PROBLEMS.  307 

Find  the  interest  on  the  following : 

6.  $550  for  1  yr.  3  mo.  at  6  %. 

7.  $250  for  2  yr.  4  mo.  at  8  %. 

8.  $300  for  3  yr.  6  mo.  at  7  %. 

9.  $160  for  1  yr.  2  mo.  at  6  % 

10.  $6  for  5  yr.  9  mo.  at  6  % 

11.  $1.50  for  3  yr.  6  mo.  at  3%.^ 

12.  $4.75  for  4  yr.  3  mo.  at  4  %. 

13.  $890  for  3  yr.  7  mo.  at  10  %. 

Find  the  interest  on  the  following : 

14.  $200  at  6  %  from  Oct.  12, 1860,  to  June  12, 1862. 

15.  $300  at  5  %  from  May  10, 1864,  to  Aug.  10, 1865. 

16.  $250  at  8  %  from  July  15, 1865,  to  Oct.  15, 1867. 

17.  $175  at  6  %  from  Jan.  16, 1866,  to  May  16,  1869. 

18.  $405  at  7  %  from  April  10, 1868,  to  June  10, 1870. 

19.  $750  at  5  %  from  Nov.  15, 1870,  to  Nov.  30, 1872. 

20.  $840  at  6  %  from  April  10, 1872,  to  May  20, 1875. 

21.  $25  at  6  %  from  June  5,  1873,  to  July  20,  1879. 

22.  A  loaned  B  $300  on  his  note  at  6  %  for  3  years. 
When  the  note  was  due  B  paid  $40,  and  gave  a  new 
note  at  the  same  rate  of  interest,  running  1  year,  for 
the  balance  then  due.  This  note  he  paid  at  maturity. 
How  much  interest  did  B  pay  for  his  $300? 


308  ELEMENTARY  ARITHMETIC. 

METRIC   SYSTEM  OF  WEIGHTS  AND  MEASURES. 

The  metric  standard  for  the  measurement  of  distances  is  the  Meter, 
which  is  39.37  inches  long  (very  nearly  3  feet  3f  inches).  From  the  meter 
all  other  measures  of  this  system  are  derived,  and  hence  the  name 
Metric  System.  Since  the  meter  is  divided  decimally,  the  system  is 
simple  and  convenient.  Ten  units  of  a  lower  order  make  one  of  the 
next  higher  in  any  measure.  Scientists  use  the  metric  system  almost 
universally. 

The  pupil  can  easily  make  for  himself  a  meter  stick  by  cutting  a  stick 
3  feet  3|  inches  long.  If  this  be  divided  by  cross  lines  into  ten  equal 
parts,  one  part  will  be  a  decimeter  (dm.).  Dividing  the  dm.  into  ten 
equal  parts  will  give  the  centimeter  (cm.),  and  dividing  the  cm.  into  ten 
equal  parts  will  give  the  millimeter  (mm.).  This  last  division  the  pupil 
need  not  make  at  first. 

Let  him  make  a  cubic  box  whose  inside  edge  is  measured  by  a  dm., 
and  he  will  have  a  Liter  Measure,  the  unit  of  liquid  and  dry  measure. 
Let  him  make  a  small  cube  whose  edge  is  measured  by  a  cm.  and  he  will 
have  the  size  from  which  the  Gram,  the  unit  of  weight,  is  determined 
(A  cubic  cm.  of  pure  water  is  the  weight  of  the  gram.) 

TABLE  OF  LINEAR  MEASURE. 

10  milli-meters  =  1  centimeter. 

10  centi-meters  =  1  deci-meter. 

10  deci-meters  =  1  Meter. 

10  meters  =  1  deka-meter. 

10  deka-meters  =  1  hecto-meter. 

10  hecto-meters  =  1  kilo-meter. 

10  kilo-meters  =  1  myria-meter. 

Compare  with  the  decimal  notation : 

1  -  ..  15 


Names  of  Orders 
used  in  Notation  and 


V  9    a 

Numeration.  5    §    e    »  5      *j    I    I 

00000*000 


Corresponding  Names   *  ji  -2  j| 

applied  to  Metric  2  "8    |    2 

Linear  Measure.  s   f|  ! 


|       |  i  I 

«       i   g  3 

a     -5  s  s 


Additional  metric  tables  may  be  constructed  by  substituting  liter  for 
meter,  grain  for  meter,  etc.  Applications  can  be  given  by  simple  examples 
easily  made  or  readily  selected. 


ANSWERS. 


42.      2.    47.      3.   61. 

4.    63. 

5.    53. 

10.    56.      11.    67. 

12.    89. 

13.    66. 

Page  49.  Article  61.  — 1. 
6.  56.  7.  96.  8.  95.  9.  46. 
14.   86.      15.    75.      16.    75. 

Page  52.  Article  66.  — 1.  180.  2.  189.  3.  180.  4.  189.  5.  190. 
6.  189.  7.  190.  8.  188.  9.  219.  10.  187.  11.  190.  12.  186. 
13.    190.      14.    185.      15.    189.      16.    190.      17.    189.      18.    200. 

Page  54.  Article  69.  Vertical  Columns.  — 1.  59.  2.  61. 
3.    50.     4.  69.     5.  50.     6.  60.     7.   58.     8.   59.     9.  49.     10.   60.     11.   60. 

12.  51. 

Page  54.  Article  70.— %1.  590.  2.  490.  3.  500.  4.  498.  5.  599. 
6.    509.     7.  499.     8.    589.     9.    600.     10.    501. 

Page  58.  Article  73.  — 1.  397.  2.406.  3.388.  4.380.  5.398. 
6.    422.     7.    395.     8.    370.     9.    369.     10.    488. 

Page  59.  Article  74.  — 1.  499.  2.  489.  3.  492.  4.  500.  5.  487. 
6.    399.     7.   400.     8.   490.     9.    500.     10.    509. 

Page  59.  Article  75.— 1.  47  c.  2.  11  c.  3.  $28.  4.  $2.  5.  28 or. 
6.  21c.     7.  81  ft.  and  99  ft.     8.   15  c.  and  7|  c.    9.   60  c. 

Page  62.  Article  77.  — 1.  500.  2.  600.  3.  599.  4.  609.  5.  508. 
6.    502.     7.   589.     8.   590.     9.    609.     10.   597.     11.   509.     12.   580. 

Page  63.     Article  78.  — 1.  701.     2.  609.    3.  590.    4.  700.    5.  690. 

6.  600.     7.   681.     8.   691.     9.  582.     10.  691.     11.   710.     12.   790. 
Page  63.     Article  79.  — 1.  25  c.     2.  52  c.     3.  25  hrs.     4.  36  pupils. 

5.  79  shingles.     6.   21c.     7.   67  c.     8.    10  ft.  and  6  ft.    9.    15  c.  and  10  c. 

10.  5  packages. 

Page  78.     Article  22.  —  2.  33  p.    4.   18  qts.    5.   8  gals.    6.  4f  yds. 

7.  7  spools  and  8  spools,  3  c.  rem.       8.    15  A.       9.   4|  hrs.       10.   9flbs. 

11.  |  pks.     12.    40  qts. 

Page  80.     Article  23.  — 1.  598.     2.  539.     3.  583.     4.  413.     5.  608. 

6.  601.     7.    410.     8.    590.     9.    548.     10.    580. 

Page  80.  Article  24.  — 1.  599.  2.  639.  3.  590.  4.  638.  5.  482. 
6.    609.     7.   519.     8.    660.     9.    510.     10.    606. 

Page  81.  Article  25.  — 1.  590.  2.  690.  3.  590.  4.  611.  5.  609. 
6.    591.     7.    621.     8.    599.     9.    603.     10.    700. 

Page  81.     Article  26.— 1.   $71.        2.   $102.        3.   $11.        4.  $40. 

5.  16  qts.     6.    82  p.     7.  $65.     8.    64  mi.     9.   $42.     10.    91  ft.      11.   42  ft. 
Page  83.     Article  27.  — 1.  612.    2.  630.    3.  793.    4.  610.    5.  711. 

6.  681.       7.    703.       8.    617.       9.    611.       10.    603.       11.    790.       12.    811. 

13.  608.      14.   591. 

Page  84.  Article  29.— 1.  702.  2.  619.  3.  711.  4.  720.  5.  802. 
6.  710.  7.  721.  8.  630.  9.  691.  10.  709.  11.  709.  12.  712. 
13.    518.       14.   595. 

Page  87.  Article  31.  — 1.  $5.12.  2.  $6.78.  3.  $6.20.  4.  $6.90. 
5.   $5.85. 

Page  88.  Article  32.  — 1.  $21.26.  2.  $19.55.  3.  $7.00.  4.  $3. 
5.   $14.      6.   $1. 

Page  88.  Article  33.— 1.  $1.  2.  $32.  3.  $1.50.  4.  $40,  $10. 
5.  $8.05.  6.  5£  yds.  7.  66  h.  w.  8.  4  yds.  9.  3  boxes.  10.  $8.60. 
11.    301  ft. 


Copyright,  1895,  by  Silvbb,  Bubdett  and  Company. 


310  ANSWERS. 

Page  89.  Article  34.— 1.  608.  2.  591.  3.  501.  4.  609.  5.  609. 
6.    569.     7.    600.     8.    601. 

Page  90.     Article  34  (continued).—  9.   689.       10.   610.  11.   691. 

12.  617.     13.    607.      14.    531.      15.    851.      16.    509.      17.    579.  18.    561. 

19.  596.     20.   600.      21.   610.      22.    681.      23.    698.      24.    696. 

Page  91.  Article  36  —  1.  118.  2.  229.  3.  229.  4.  219.  5.  210. 
6.    229.       7.    119.       8.    206.       9.    208.       10.    108.       11.    218.       12.    109. 

13.  218.     14.  317.     15.    178.     16.   128. 

Page  92.     Article  36  (continued).  — 17.    139.       18.    118.  19.    28. 

20.  27.  21.  109.  22.  124.  23.  25.  24.  29.  25.  117.  26.  117. 
27.  45.  28.  53.  29.  117.  30.  127.  31.  12.  32.  34.  33.  147. 
34.  136.  35.  26.  36.  23.  37.  106.  38.  116.  39.  26.  40.  61. 
41.  116.  42.  123.  43.  24.  44.  29.  45.  114.  46.  122.  47.  35. 
48.  9.  49.  125.  50.  135.  51.  48.  52.  87.  53.  106.  54.  89.  55.  91. 
56.    71.     57.    108.     58.    59.     59.    97.     60.    69.     61.   45. 

Page  92.  Article  37.  — 1.  5  mi.,  30  mi.  2.  $40.  3.  $51.  4.  92  c. 
5.    198  or.        6.    $105.       7.    $145.       8.    100  tr.       9.   229  tr.         10.    991. 

11.  $299.       12.    294  ft. 

Page  95.  Article  41.  — 1.  6008.  2.  6095.  3.  6767.  4.  6008. 
5.    6760.     6.    6712. 

Page  96.     Article  41  (continued).  —  7.   6118.       8.   6120.       9.  6092. 

10.  6108.     11.    5921.     12.    5908. 

Page  96.     Article  42.  — 1.   7  qts.     2.   3£  pks.     3.  30  da.  4.   $36. 

5.   3  s.     6.    24  pt.  bottles.     7.   4  da.     8.   144  mi.     9.   $168.     10.  640  pairs. 

Page  97.     Article  43.  — 1.   4089.       2.   4898.       3.   6798.  4.  2889. 

5.    5989.     6.   3989.     7.    8809.     8.   3708.     9.   4987.     10.   2879.  11.   4896. 

12.  2999.  13.  1809.  14.  3895.  15.  4889.  16.  5987.  17.  7899. 
18.  6909.  19.  4789.  20.  4478.  21.  6818.  22.  6078.  23.  4799. 
24   4989. 

Page  97.  Article  44.  — 1.  6110.  2.  6782.  3.  6073.  4.  5960. 
5.  6063.  6.  4308.  7.  6000.  8.  5788.  9.  5206.  10.  5990.  11.  5298. 
12.  5000.  13.  6776.  14.  6120.  15.  5606.  16.  5120.  17.  6727. 
18.    5608. 

Page  98.  Article  45.  —  1.  21  c.  2.  60  mi.  3.  $2.  4.  $260. 
5.   42  marbles.      6.    $28.      7.    $34.50.      8.   31  ft.      9.    $300.      10.    190  sh. 

11.  $2.25.  12.  250  shingles.  13.  $78.50  horse  cost,  $39.25  cost  of  cow, 
$39.25  left. 

Page  109.  Article  17.  — 1.  45  bu.  2.  35  ad.,  7  ad.  left.  3.  49yrs. 
4  12  bu.  5.  31  c.  6.  42  wheels.  7.  1  bu.  8.  42  pickets.  9.  6  c. 
10.  35  leaflets.  11.  24  oz.  12.  6oz.  13.  15  lbs.  14.  5  lbs.  15.  10^  lbs. 
16.   16.     17.  39.     18.  25.     19.   8.  '  20.  36.     21.   7.     22.   4  times.     23.  42. 

Page  111.  Article  18.  — 1.  4056.  2.  5488.  3.  7110.  4.  4818. 
5.    5118.     6.    5802. 

Page  112.  Article  19.  — 1.  3919.  2.  4490.  3.  3601.  4.  5159. 
5.   4000.     6.   4909. 

Page  112.  Article  20.  —  1.  60  hrs.  2.  180  sec.  3.  $3.40.  4.  2598  bu. 
5.    $420.     6.   3500  cans.     7.  $320.     8.  $550.     9.   600. 

Page  114.  Article  22.  — 1.  4076.  2.  4917.  3.  7890.  4.  5878. 
5.    8088.     6.    4987.     7.    8895.     8.    7789.     9.    4876.     10.    9007.      11.    4909. 

12.  8889.  13.  5807.  14.  2909.  15.  5887.  16.  8798.  17.  3976. 
18.    4869. 

Page  114.  Article  23.  — 1  5281.  2.  5690.  3.  4100.  4  5090. 
5.    4090.     6.    4290. 

Page    115.      Article    24.  — 1.   \  of  the  money.     75  c.  2.   $45. 

3.  16  qts.  4.  $  of  a  melon.  5.  lo|pts.  6.  57  marbles.  54  marbles 
Frank  has.     7.    140  ft.     8.    $4.25.     9.    $560.     10.    370  ft. 


ANSWERS.  311 

Page  116.  Article  25.  — 1.  5741.  2.  5690.  3.  5999.  4.  6096. 
5.  5400.  6.  5001.  7.  5510.  8.  5699.  9.  4021.  10.  4130.  11.  5941. 
12.    5920.     13.    4829. 

Page  117.  Article  26.  — 1.  7679.  2.  7080  3.  7998.  4.  5790, 
5.  8919.  6.  7987.  7.  3897.  8.  2857.  9.  4979.  10.  4809.  11.  5099. 
12.  3989.  13.  8896.  14.  1608.  15.  6806.  16.  6896.  17.  4999. 
18.    1968. 

Page  117.  Article  27.  — 1.  $5.90.  2.  $108  for  fruit-trees,  $210  for 
shade-trees.     3.    $600.     4.    $889.     5.    175.     6.    35  yrs.     7.    450. 

Page  119.  Article  29.  — 1.  5222.  2.  4629.  3.  4922.  4.  5222. 
5.    5890.     6.    6021.     7.    5100.     8.    5900.     9.    5191.     10.    7282. 

Subtract:  1.  7099.  2.  7767.  3.  3965.  4.  3898.  5.  6509.  6.  2989. 
7.    4987.     8.    3869.     9.    6999.     10.    1996. 

Page  120.  Article  30.  — 1.  5255.  2.  5555.  3.  5733.  4.  6409. 
5.  5210.  6.  5933.  7.  5030.  8.  6330.  9.  6091.  10.  5218.  11.  6023. 
12.    5234. 

Page  121.  Article  31.— 1.  687  mi.  2.  $4459.  3.  $759.  4.  1904, 
1914,2044.     5.    $2015.     6.    86  bbls.*   $417. 

Page  122.  Article  32.  — 1.  5325.  2.  5334.  3.  6101.  4.  7105. 
5.    5139.     6.    5690.     7.    5702.     8.    5100.     9.    5900.     10.    6120. 

Subtract:  1.  6267.  2.  5769.  3.  4099.  4.  4889.  5.  4407.  6.  5777. 
7.    779.     8.    887.     9.    469.     10.    1789.     11.    4387.     12.    3098. 

Add:  1.    7009.      2.    6099.      3.    6000.      4.    6009.       5.    6009.       6.    7023. 

7.  5220.     8.    6439.     9.   6122. 

Page  128.  Article  12.  — 1.  f  2.  $66.  3.  63  desks.  4.  48  ft. 
5.  65  c.  6.  63  sheep. 

Page  133.  Article  17.  — 1.  63  da.  2.  9 p.  3.  5  min.  4.  57  sq.ft. 
5.  6^  lbs. 

Page  134.  Article  17  (continued).  —  6.  4£  ft.      7.  60  qts. 

8.  9  rides.  9.  8  bu.,  32  pks  ,  48  bu.  10.  50  c.  11.  10  da.   12.  6  sides, 
54  plants.  13.  54  hrs.  14.  16  bu.  15.  4  c. 

Page  135.  Article  19—1.  5191.  2.  531 L  3.  4701.  4.  5104. 
5.  5609.  6.  6063.  7.  6233.  8.  5309.  9.  5971.  10.  6210. 

Page  136.  Article  20. —1.  5269.  2.  5569.  3.  6200.  4.  5260. 
5.  5305.  6.  5023. 

Page  136.  Article  21.  — 1.  680.  2.  2500.  3.  988.  4.  451  people. 
5.  $6.50 ;  50  c.  loss. 

Page  137.  — Add:  6.  7203.   7.  6228.  8.  5229.  9.  5220.  10.  7121. 

Page  138.  Article  22.  — 1.  5478.  2.  4558.  3.  4788.  4.  5290. 
5.  5420.  6.  6312.  7.  7102.  8.  6031.  9.  5003.  10.  5623.  11.  4332. 
12.  5200. 

Page  138.  Article  23.  — 1.  4069.  2.  15.  3.  4162.  4.  4693. 
5.  2614.  6.  3749.  7.  7555.  8.  3595.  9.  666.  10.  2706.  11  2576. 
12.  4767.  13.  3687.  14.  4288.  15.  3258.  16.  169.  17.  868. 
18.  4969.  19.  2989.  20.  1099.  21.  4596.  22.  6569.  23.  3999. 
24.  6999 

Page  139.  Article  24.  — 1.  645.  2.  385  gals.  3.  257  mi.  4.  56  bu. 
5.  $2290.  6.  $1750. 

Page  139.  Article  25.  — 1.  5303.  2.  6331.  3.  5313.  4.  6201. 
5.  7823.  6.  6919.  7.  5332. 

Page  140.  —  Find  differences :  1.  8908.  2.  7909.  3.  3896.  4.  2996. 
5.  6078.  6.  3396.  7.  1987.  8.  1639.  9.  1996.  10.  4309.  11.  3799. 
12.  1878.  13.  769.  14.  5798.  15.  8667. 

Page  140.  Article  26.  — 1.  4922.  2.  7933.  3.  5112.  4.  4093- 
5.  5144. 


312  ANSWERS. 

Page  141.     Article  27.-6.   5334.     7.   6321.      8.   7123.     9.   7204. 

10.  7122.  11.  7311.  12.  5764.  13.  4909.  14.  5489.  15  6404. 
16.  6243.  17.  6203. 

Page  141.  Article  28.  — 1.  1895  — 1492  =  403.  2  4,  6  in.  squares. 

3.  $6.60  spent,  $1.40  rem.   4.  $150.   5.  $4.73.   6.  $2.85.   7 
8.  $15.04.  9.  $7.11. 

Page  144.  Article  29.  — 1.  6342.   2.  6121.   3.  6228.  4  5108. 

5.  5898.  6.  6120.  7.  7381.  8.  6284/  9.  6248.  10.  5290.  11.  4450. 
12.  5343.  13.  6432.  14.  5531.  15.  5908. 

Page  156.  Article  20—1.  8  p.  2.  80  c.  3.  12.  4  12  c. 
5.  16  stamps*.  6.  66  c.  7.-8mos.  8.  10.  9.  96  inches.  10  8  bouquets. 

11.  8doz.  12.  37*  c.  14.  75  c.  15.  6  p.  16.  56  cu.  in.;  84  cu.  in., 
112  cu.  in. 

Page  158.  Article  21.  — 1.  7220.  2.  7113.  3.  7280.  4.  7320. 
5.  6943.  6.  7340.  7.  7210.  8.  7108.   9.  7215.   10.  8010.   11.  8133. 

12.  7132.   13.  7349.   14.  8020.   15.  5080.   16.  5203.    17.  5965. 

18.  6009.  19.  6013.  20.  5909.  21.  5201. 

Page  159.  Article  21.  — 1.  9267.   2.  5939.  3.  5659.  4.  7509. 

$.  2407.  6.  5106.  7.  696.  8.  847.  9.  60S.  10.  1628.  11.  667. 
12.  3066.  13.  2087.  14.  3628.  15.  4069. 

Page  159.  Article  22.  — 1.  6  in.  2.  12  wks.  3.  $330.  4.  $12*. 

5.  $2.75.   6.  $131.   7.  $400.   8.  50  da.   9.  30  c;  72  c.  10  $6. 

11.  1200  mi.  12.  10  pupils.  13.  $4.  14.  75  c.  15.  48  cu.  in.  blks. 
16.  $3.  17.  1661yds.  18.  $1.80. 

Page  164.  Article  6—1.  756.   2.  1712.   3.  1008.  4.  1956. 

5.  1418.  6.  1536.   7.  1960.   8.  618.   9.  4046.   10.  1972.  11.  9014. 

12.  9318.  13.  9418.  14.  936.  15.  1526.  16.  1698.  17.  698.  18.  1572. 

19.  1210. 

Page  166.     Article  8.— Divide  by  2:  1.  3699.     2.  4 124  J.     3.  4890*. 

4.  3202.     5.  3585.     6.   4705.     7.   3588.     8.   628*.     9.   3364*.      10.    1007*. 

11.  2409*.     12.   4598*. 

Page  167.     Article  10.  — 1.  4937*.     2.  3000*.    3.  4673*.    4.  3595. 

6.  1549.     6.   2864^.     7.   4050*.     8.   3950.     9.   3500*  bu.     10.   2522*  pks. 
Page  167.     Article  11.  — 1.  143  mi.      2.    156  times.     3.  326  times. 

4.  275  da.     5.   57  albums.     6.   1500  plants.     7.   840. 

Page  168.     Article  12.  — 1.  9J58.       2.  9291.      3.  8358.      4.  9018. 

5.  9738.     6.   9807.     7.   9027.     8.  7647.     9.   10107.     10.  12369.     11.  8601. 

12.  9027.     13.   8214.     14.   9324. 

Find  quotients:    1.    1229.      2.   1152.      3.   2630*.      4.    1825*.      5.   833f. 

6.  2352*.     7.   3036.     8.   2770. 

Page  168.  Article  13.  — 1.  11 83,  three-cents.  2.  833*  yds.  3.  $2061. 

4.  150  wks.  5.  834  mi.  6.  $723.  7.  $450.  8.  723,  1005,  106,  2040. 
Page  169.  Article  14.  — 1.  6013.   2.  5123.  3.  5341.   4  3921. 

5.  15092.  6.  5001.  7.  5797.  8.  5308.  9.  6333.  10.  5220.  11.  5200. 
12.  6310.  13.  7233.  14.  6102.  15.  5013.  16.  6109. 

Page  170.  Article  15.  — 1.  7999.  2.  7998.  3.  8757.  4  7859. 
5.  8396.  6.  10139.  7.  4899.  8.  6220.  9.  8538.  10.  12542.  11.  9538. 
12.  7039.  13.  3408.  14.  8637.  15.  125. 

Page  170.  Article  16—  1.  28  c.  2.3  yds.  3.  12  pks.  4.  6|  vds. 
5.  7  c.  6.  2*  yds.  7.  $3.50.  8.  $1.50.  9.  15  da.  10.  4  c.  11.  45  ft. 
12.  12pkgs. 

Page  171.  Article  18.  — 1.  3424.   2.  3912.   3.  3872.   4.  3956. 

5.  8316.  6.  8392.  7.  7904.  8.  6712. 

Quotients:  1.  1697^.   2.  533|.   3.  3502^.   4.  3800f.   5.  7758£. 

6.  16972*.  7.  8508f.  8.  9848|. 

1.  1600  bricks.  2.  5040  pks.  3.  576  sq.  in. 


ANSWERS. 


313 


Page  172.     Article  19.  —  1.   9280.     2.   13540.     3.  13825.     4.   18845. 

5.  17895.     6.   9890.     7.   9740.     8.   5335. 

Quotients:    1.   3858.       2.    18961$.       3.    6286f.        4.  3721.        5.   8688$. 

6.  7604$.       7.  9395$.       8.   7460.       9.    10861$.       10.   9492$.       11.   17836. 
12.    6948$. 

1.   1179  five-cents.     2.   60  lbs.     3.  $1970.     4.  $  of  3  times  30:  2  greater. 

5.  $36.50:  7  bills,  $1.50  in  change. 

Page  173.  Article  1.  — Express  in  figures:  1.  $967.08.  2.  $52000.12. 
3.   $41011.07.     4.   $11100.01. 

Products:  1.  $4845.     2.  $52.20.     3.  $225.05.     4.  $858.12.     5.  $1922.80. 

6.  $4.25.     7.    $3.56.     8.   $2.25.     9.   $4.50. 

Page    174.     Article    2.  —  Quotients :     1.  $83.27f  2.  $78.05j. 

3.  $233.35£.       4.   $3350. 16f.       5.  $20190.45.       6.   $6400.       7.   $5606.52$. 
8.  $3201.60.     9.   $22625. 

Page  174.  Article  3.  — Factors:  2.  36  =  6  X  6,  4  X  9,  2  X  18, 
3X12;  28  =  4X7,  2X14;  45  =  9X5,  3X15;  48  =  3X16, 
4  X  12,  6  X  8,  2  X  24;  50  =  2  X  25,  5  X  10.  4.  18  =  2  X  3  X  3; 
24  =  2X3X4;  27  =  3X3X3;  28  =  2X2X7;  30  =  2X3X5; 
32  =  2X4X4;  40  =  2X4X5;  45  =  3X3X5. 

Page  175.  Article  5.  — Multiply:  1.  59244.  2.  18054.  3.  60408. 

4.  35442.  5.  52074.  6.  71688.  7.  43848.  8.  35382.  9.  96522.  10.  62376. 
11.  77748.  12.  70614. 

Divide  :  1.  5405.  2.  5808$.  3.  6306$.  4.  7407$.  5.  7807f .  6.  8208$. 
V  9409$.  8.  9709f.  9.  9576.  10.  2861|.  11.  3198$.  12.  5238|. 
Page  176.  Article  6.  — 1.  $1.92.  2.  386  lbs.  3.  981  mi.  4.  $5.88. 


5.  2190  da. 

Page  176. 
5.  158010.  6. 

Page  177. 


-1.  4702.   2.  6322.   3.  6013.   4.  70219. 


Article  7. 

63223. 

Article  8.  — 1.  23789.  2.  13497.  3.  17905.  4.  23907. 
5.  30886.  6.  42087.  7.  56708.  8.  67278.  9.  63979.  10.  17598.  11.  44997. 
12.  30497.  13.  21989.  14.  44708.  15.  42999.  16.  26879.  17.  23395. 
18.  8498. 

Page  177.  Article  9.  — 1.  $13.63.  2.  9500.  3.  1789.  4.  205  bu. 
5.  $153.40.  6.  8  strips.  7.  $337  lost.  8.  $9.54.  9.  $779.  10.  1199  mi. 

Page  178.  Article  10.  — 1.  14$  c.  2.  45  min.  3.  36  c.  4.  f  bu. 
24  qts.  5.  4  times.  6.  9  horses.  7.  28  c.  8.  41f  c.  9.  \.  10.  9  c. 
11.  9  yr.  12.  14  lbs.,  7  lbs.,  If  lbs.  13.  15  mi.  14.  72  c.  15.  $1 .44,  $3.36. 


Page  180.  Article  12.  — 1.  7223.  2.  5033. 

5.  49003.  6.  53013.  7.  8131.  8.  6033.  9.  6230. 

Page  180.  Article  13.  — 1.  6500.  2.  $7.50. 
5.  $782. 

Page  181.  Article  14.  — 1.  5340.  2.  6344. 

5.  54033.  6.  50172.  7.  6343.  8.  7031.  9.  8422. 

2.  3899  the  smaller. 


3.  6321. 
10.  6833. 
3.  $659. 


4.  7210. 


4. 


$240. 


7011. 
8123. 
7999. 


4.  7334. 


7100.   2.  5542.   3.  7135.   4.  49245. 


Page  182.  — 1.  $12.43. 
5.  $10.53. 

Page  182.     Article  15.  —  1 
5.  42526.      6.   61323. 

Page  183.  — 1.  $5117.     2.  500*  mi.     3.  $1734. 

Page  183.     Article  16.  — 1.  10  c.     2.  25  pict. 
5.   2  c.     6.  48  sq.  ft.      7.   $2.50.      8.   5  c.      9.  56  wk.,  28  wk. 
11.   12  ft.     12.   96  cu.  in. 

Page  185.    Article  18.  — 1.  48636.     2.  40383.     3.  66395 
5.   42686.     6.  48559.     7.   75383.     8.    83258. 

Divide:  1.  2791f     2.  2578*.     3.  2546f     4.  5664.     5    2651$. 


4.  30  suits. 
3.  4  books. 


5.  $209. 

4.  $1.00. 

10.  $1.40. 


4.  55342. 


7.  7851.  8.  1943f.  9.  3945f.  10.  2542f  11.  9715f  12.  9609f 


6.  4051f 


314 


ANSWERS. 


3.  S2.50  loss. 


Page  185.    Article  19—1.  $1.25.         2.  $2430. 

4.  $467.     5.  $271. 
Page  186.     Article  20—1.   6414.      2.  7377.      3.  7443.      4.  5231. 

5.  53023.     6.   52124. 

Page  186.    Article  21.  —  1.  21986.     2.11457.     3.41998.    4   21789. 

6.  30990.  6.  57337.  7.  51543.  8.  41644.  9.  31358.  10.  61675. 
11.  42786.  12.  10227.  13.  30988.  14.  15798.  15.  93389.  16.  90796. 
17.   13468.     18.    11939. 

Page  187.  — 1.  $10.15.     2.  $22.95.     3.  156  yrs.     4.  179  lbs.     5.  $4750. 
Page  188.    Article  23.  —  1.  210  =  2  X  3  X  5  X  7.     2.287  =  41X7. 

3.  246  =  2  X  3  X  41.  4.  312  =  2  X  2  X  2  X  3  X  13.  5.  390  =  2  X  3 
X  5  X  13.  6.  486  =  2  X  3  X  3  X3  X3  X3.  7.  546  =  2X3X7  X  13. 
8.594  =  2X3X3X3X11.  9.684  =  2X2X3X3X19.  10.615  = 
3  X  5  X  41.  11.  714  =  2  X  3  X  7  X  17.  12.  819  =  3  X  3  X  7  X  13. 
13.873=3X3X97.     14.910  =  2X5X7X13.     15.987  =  3X7X47. 

Page  189.  Article  24.  — 1.  7333.   2.  6535.   3.  6445.   4.  7213. 
5.  53542.  6.  53324. 
Page  189.  Article  25.  — 1.  42653.  2.31786.  3.11987.  4.21289. 

5.  63909.  6.  41999.  7.  22863.  8.  86886.  9.  78000.  10.  65529. 
11.  55476.  12.  51919. 

1.  $10.80.  2.  $5.60.  3.  $5.25.  4.  $12.7 
Page  190.  Article  26.  — 1.  7466.  1 

6.  62431.  6.  62061.  7.  4402. 
Page  190.  Article  27.  — 1.  23668.  2.  22989.  3.  3883.  4.  12635. 

5.  4819.  6.  65995.  7.  14886.  8. 
Page  190.  Article  28. —  1. 

4.  $20.  5.  $1.50.  6.  27  c.  7.  9  c.  8.  30  mm.,  1  hr.  9.  54  c,  6  times. 
10.  \  doz.,  ft,  15  c.  11.  $1.68.  12.  $3.92.  13.  14  bbls.  14.  $1.70. 
15.  $9.  16.  48  1b.  17.  f,  30  c.  18.  $1.20.  19.  f 

Page  192.  Article  30.  —  Multiply  :  1.  30792.  2.  68312.  3.  55656. 

4.  75072.   5.  51072.   6.  31576.    7.  48752.    8.  59864.   9.  69192. 

10.  47784. 
Divide:  1.  5180|.  2.  6456f  3.  70571   4.  7282f. 

7.  3627f.  8.  9857|.  9.  7851.  10.  4876f. 
Page  192.  Article  31.  —  1.  30  c.  2.  8  pails.  3. 

5.  5  c.  6.  219  T.  7.  39  bbls. 
Page  193.  Article  32.  — 1.  7662. 

5.  7364.  6.  51652.  7.  52313. 

Page  194.  Article  33.  — 1.  21443.  2.16265.  3.31416.  4.43887. 
5.  24652.    6.  7071.    7.  70798.   8.  18756.   9.  15127.   10.  53799. 

11.  58236.   12.  70168. 
Page  194.  Article  34.  — 1.  $8.89. 


6621.   3.  7314.   4.  6630. 


23668.  2.  22989. 
61998.  9.  79933. 
4.    2.  4J  c,  371  c. 


3.  f,  h  12  c. 


5.  $2400. 
Page  195. 

6.  8200. 
Page  195.     Article  36—1.  7777. 

5.   61644.     6.   62142.     7.   8200. 
Page  196.     Article  37.  — Multiply 


5.  2673|.  6.  4879f 
15  da.     4.  09  sheep. 
2.   6546.      3.   8166.       4    8663. 


2.  $18.12.     3.  $25.28.     4.  $9.73. 


Article  35.  — 1.  7777.  2.  57522.  3.  61644.  4.  62142. 


2.  6283.   3.  5566.   4.  57522. 


4.  72063.  5  57582. 

10.  44622.  11.  61866. 

16.  81045.  17.  73449. 

22.  24831.  23.  76167. 

Divide:  1.  1715|.  2. 

7.  1504$.  8.  4949£. 

13.  4347£.  14.  32341. 


1.  75951.  2.  63855.  3.  57546. 
6.  53712.  "7'.  57366.  8.  42642.  9.  61506. 
12.  33822.  13.  77823.  14.  84384.  15.  43533. 
18.  67167.  19.  57501.  20.  76284.  21.  5G*>82. 
24.  34866.  25.  57942. 

1985|.  3.  3040f .  4.  8039.  5.  1236|.  6  6156f. 
9.  9825|.  10.  8478.  11.  7570f  12.  5284f 
15.  2709f.   16.  7343$.   17.  8402f.   18.  7136. 


ANSWERS. 


315 


19.  5897$.  20.  4896.  21.  4581. 
25.   3235§.     26.   2263.     27.   2528$. 

Page  196.  Article  38.  — 1. 
108,54,  81.     4.   $7.20.     5.   $62.26. 

Page  197.     Article  39.  — 1. 


22.  5062 

28.  39101 
10  sq.  yds. 

6.  $920. 
78883.  2.  73512. 


23.  9894$. 
29.  6172$. 
2.  $12.96. 


24.  8480$. 
30.  4938f. 
3.  72,  99,  63, 


Page  197.  Article  40.  —  1.  85795.  2.  47086. 
5.  59714.   6.  30437.   7.  54442.   8.  9754.   9.  78756. 
11.  7963.  12.  59658.  13.  85018.  14.  8875.  15.  82355. 

Pages  197,  198.  Article  41.  — 1.  $1.69,  $15.21.  2 
3.  76  mo.,  6£  yrs.  4.  $7840.  5.  $679.  6.  $37.05.  7. 
8.  10  yds.  9.  $16.12.  10.  $6.30.  11.  $1638. 

Page  202.  Article  6.  —  Multiply  by  11:  1.  986953. 


3.  36057.  4.  76687. 
10.  60134. 


30  dress  p. 
$51.47  loss. 


9140736.   4.  4343427 
8.  5280203. 

Divide  by  11:  1.  2347T9T. 
5.  25778r\.   6.  17273TV 
10.  890950^.  11.  217712/T, 


5.  4235517. 

2.  1858T3T. 
7.  51618T\. 
12.  176225T4T. 


6.   6928625. 

3.   3439T9T. 
8.   81859fT. 


2.  715539. 
7.  8235623. 

4.  81782T2T. 
9.  36730}^. 


Pages  202,  203,  204.  Article  7.  — 1. 


$24.  2.  36  bu.  3.  12  da. 
\.  9.  $0.84.  10.  $2.00. 
12  da.  15.  $48.  16.  $,  -$, 


2.  31  p.   3.  3648.   4.  4015  da. 


4.  $6.  5.  $64.  6.  $1.40.  7.  J.  8. 
11.  $8  00,  $8.50.  12.  $0.32.  13.  $1.50.  14. 
$63.  17.  12  squashes. 

Page  204.  Article  8.  — 1.  $835 

5.  $21.90. 
Page  205.  Article  9.  — Products:  1.  93708.  2.  113868.  3.  91416. 

4.  111408.  5.  358176.  6.  8754252.  7.  574032.  8.  475764.  9.  7649976. 

10.  4194312.  11.  814188.  12.  6828036.  13.  7417128.  14.  2288736. 
15.  8740764.  16.  10264272. 

Quotients:  1.  532.  2.  264.  3.  2462f  4.  8195TV  5.  4532T\.  6.  7286. 
7.  4139T\.  8.  6953£.  9.80903.  10.  40331 }.     11.  24864TV  12.  4031 3f 

13.  6553776|.  14.  9259251-f.  15.  8333333}.  16.  2974085}|. 
17.  2079139§.  18.  7173216TV  19.  82166704}.  20.  63182703. 
21.  80640780}.    22.  54440445|.    23.  39890833}|.   24.  57728881}!. 

Page  206.  Article  10. —  1.  224  doz.  prs.   2.  $435278.  3.  420656 
tons.  4.  80  bbls.  5.  1440  da.  6.  4400  rev. 

Page  207.  Article  12.  — 1.  $19.68.    2.  $15.57. 

4.  $43.36.  5.  $83.06. 
Page  208.  Article  13.  — 1.  887.   2.  1177.   3.  1175. 

5.  1176.  6.  1178868.  7.  1177579.  8.  1227742. 

Subtract:  1.  654222.   2.  79419984.   3.  827271371.   4.  80271568. 
5.  66699043.  6.  789903201. 

Page  209.  Article  15.  — 1.  1838122.  2.  3961922. 
4.  1653624.  5.  1781582.  6.  5047012.  7.  7410855. 
9.  6133124.   10.  2254008.   11.  1865626.   12.  6193205. 

14.  2430490.   15.  2722533.   16.  3117442.   17.  3478296. 
19.  2045780.   20.  3472598.   21.  1504760.   22.  4048806.   2J 
24.  1644984. 

Page  210.  Article  16.  —  Quotients :  1.  320.    2.  112. 
4  213.   5.  113.   6.  213.   7.  230f   8.  560.   9.  568£. 

11.  230£.  12.  223^.  13.  211$.  14.  230.  15.  312. 
17.  250.  18.  242TV  13.  340.  20.  420^.  21.  452}$. 
23.  2210£.  24.  2112. 

Pages  210,  211.  Article  17—1.  $576.44.  2 
4.  1728  cu.  in.  5.  $346.75.  6.  $1950.  7.  $108.  8. 
aq.  yds. 

Page  211.  Article  18.  —  1.  604  —7  rem.  2.409. 


3.  $103.20. 
4.  1173. 


3. 
8. 
13. 
18. 


1278118. 
7649562. 
978342. 
3427664. 
8109720. 


3.  223. 

10  320. 

16.  352TV 

22.  1320£. 


$8.   3  $15.96. 
1750  sq.  ft.,  194| 

3.  403  -  3  rem. 


221 


316  ANSWERS. 

4.  706.  5.  709  — 4  rem.  6.  501.  7.  C05  —  47  rem.  8.  304  — 13  rem. 
9.   709  — 49  rem.     10.   408  — 1  rem.     11.   908.     12.   502  — 16  rem. 

Page  212.     Article  19.  — 1.  331  A.    2.  $50.     3.  57216.    4.  $35.70. 

5.  1  o'clock,  p.  m.,  252  mi.  Note.  8  mi.  gain  in  1  hr.,  56  mi.  to  be  gained; 
56  mi.  -r  8  mi.  =  7  (times) ;  7  hrs.  to  gain  56  mi. ;  36  mi.  X  7  =  252  mi.; 
6  a.  m.  +  7  hrs.  as  1  P.  M.      6.   610. 

Pages  212,  213.  Article  20.  — 1.  50  da.  2.  ^,  36  A.  3.  $0.12. 
4.  $14.  5.  240pkgs.  6.  $3.80.  7.  $2.35.  8.  $3.  9.  $0.50,  $0.40, 
$0.15,  $1.05.     10.   $30.     11.    1,4,9,16,25,36,49,64,81,100. 

Page  214.  —  Products :   1.   842060.  2.    1,420.048.  3.   2910042. 

4.  3,457,472.      5.   2856442.        6.   2363833.        7.   2,382,362.        8.  3356878. 

9.  2430462.  10.  2027712.  11.  202200.  12.  4803089.  13.  1305664. 
14.   2007573.     15.    1065084.     16.  4730646.     17.  4738722.     18.   2968896. 

Pages  214,  215.  Article  22.  — 1.  $3.48.  2.  1895  —  1861  as  34  vrs. 
3.  $399.     4.  $7.80  gain.     5.   $307.80.     6.  $851.84.     7.   $22.30. 

Page  215.  Article  23.  —  Quotients :  1.  1245.  2.  1617.  3.1303  — 
274  rem.  4.  441 —479  rem.  5.  2121.  6.  1657  — 361  rem.  7.  1(.)I5. 
8.  1627.  9.  1071— 55  rem.  10.  1107  —  488  rem.  11.  1123.  12.  220  — 
863  rem.  13.  2432.  14.  1561.  15.  1227— 316  rem.  16.  2696  — 68  rem. 
17.  589 -125  rem.     18.  778  —  123  rem. 

Pages  215,  216,  217.     Article  24.  — 1.  $136.98$$.  2.  $375. 

3.  6480.  4.  120,000  people,  200  votes.  5.  $1.61. 

6.  20  vrs.  7.  259387166.  8.39600  ft.  9.  Yes.  18750 
mi.  10.  6912  cu.  in.  11.  596661.  12.  8  c.  13  368400 
watches.  14.  $46,800,000.  15.  1152  pounds,  $345.60. 
16.  375.     17.  114$  yds.     2d  Ans.  193§  yds. 

Page  218.     Article  25.  — 1.  4164-144  rem.        2.  1555  —  20  rem. 

3.  5094  —  91  rem.  4.  38558  —  127  rem.  5.  41463  —  18  rem.  6.  4708  — 
145  rem.  7.1345.  8.  10899  — 146  rem.  9.  3086  — 193  rem.  10.26530 
—  14  rem.     11.  15696 -63  rem.     12.  3986  — 19  rem.     13.  5398  — 201  rem. 

14.  1625  — 208  rem.  15.  3478  — 10  rem.  16.  7927- 131  rem.  17.  60  — 
180rem.  18.  3224  -  104  rem.  19.  3692  — 144  rem.  20.  5033  — 135  rem. 
21.8060.     22.  79612  — 112  rem.     23.  1477  — 285  rem.     24.  7029  — 430  rem. 

Page  218.    Article  26.  — 1.  $0.64.    2.  180  ft.    3.  $2.40.    4.  144  mo. 

5.  6  score.        6.  ^,  40  A.,  56  A.        7.  $144.        8.  $1.98.       9.  80  apples. 

10.  $33.33$.      11.   198  sq.  ft.,  22  yd.      12.  $12.      13.   $35.20.      14.   11  da. 

15.  $144,  $72.     16.  $2.     17.   11  qts.     18.  $2.40,     900,      900. 

Page  220.    Article  27.  —  1.  $43.20.    2.  1512 sq.ft.,  S9j. 76.    3.120ft. 

4.  15  hrs.  20  min.     5.  47520  ft.     6.   1816  to  1830.     7.  5,346,583  bales. 
Page  221.     Article  28.  — 1.  203  —  537  rem.  2.  314  -  79  rem. 

3  286  — 4899  rem.  4.  569  —  5758  rem.  5.  1445 —  3062  rem.  6.  7279  — 
715-rem.     7.  135  —  1766  rem.     8.   19885  —  1244  rem.     9.  325  —  2073  rem. 

10.  368-2017  rem.  11.  503 -3408  rem.  12.  2182  -  529  rem.  13.260 
-8117  rem.  14.  1459  -  1764  rem.  15.  888  —  983  rem.  16.4748  — 
3537  rem.  17.  194  — 559  rem.  18.  884  — 1791  rem.  19.  520  — 4982  rem. 
20.  430  -  4283  rem.  21.  798  -  7935  rem.  .  22.  354  —  2571  rem. 
23.   121,397  —  370  rem.       24.  9869  —  386  rem.  , 

Pages  221  to  224.  Article  29. —  1.  133  States,  1005  sq.  mi. 
2.  60  lbs.        3.  1925  mi.        4.  9396  bu.,  1604  bu.  rem.        5.   8067  cu.  ft. 

6.  $6,187,236,753.  7.  $3025.  8.  805  bells.  9.  (a.)  270  sq.  ft.  parlor, 
195  sq.  ft.  bedroom,  252  sq.  ft.  sitting-room,  210  sq.  ft.  kitchen,  180  sq.  ft. 
dining-room,     (b.)   $110.95  cost,     (c.)  $9.60  cost  of  molding.     10.   86  yrs. 

11.  23  payments.  12.  8993  towns.  13.  4701  §  loads.  14.  14  tons. 
15.  $16.24f.  16.344,030,166.  17.  17  yrs.  18.  17 7|  loads.  19.  $599,720, 
20.   128792  lbs.     21.   306000  lbs      153  tons. 


if,  if 

»•  if 


ANSWERS.  317 

Page  225.  Article  33.  — 1.  6.  2.  6.  3.  18.  4.  13.  5.  16.  6.  3. 
7.  9.     8.   2.     9.   14.     10.  39.     11.   12.     12.  25.      13.  25.     14.  6.     15.  72. 

16.  14.     17.   7.     18.  16.     19.  7.     20.   12.     21.  25. 

Page  227.     Article  37.  — 1.  3024.        2.  504.        3.  3744.  4.  288. 

5.  504.  6.  594.  7.  540.  8.  2376.  9.  180.  10.  357.  11.  2709. 
12.  720.      13.    1,340,480.      14.   17,670,120.       15.   376,216.      16.  7,266,480. 

17.  1,825,824.  18.  223344.  19.  2016.  20.  1440.  21.  14112. 

Page  228.     Article  40.  — 1.  2J|.     2.  2jf.     3.  4£.    4.  5|.    5.  5  A- 

6.  2f     7.  40.     8.  9.     9.   18. 

Page  229.  Article  41.  —  2.  5  pairs.  3.  47£  lbs.  4.  23|  yds. 
5.  $40^.     6.  22  bu.     7.  30  lbs. 

Page  232.     Article  7.  — 1    W.        2.  4U.         3.  %9.         4.  4£*. 

5.  124*        6<    1A7J>.       7.    1^28.        8>     2L41  9.     2A5A  10.     l||i,        11.     2|il 

12.  4fo4   13  W   i4.  w.   15.  ijjjji.   16.  ijjjA.   i7.  8|f2A 

18.  fllljijta. 

Page  232.    Article  8—1.  *f.     2.  1*1.     3.  If*.    4.  *4*.     5.  ±J*. 

6.  Sjf. 

Page  233.     Article  9.  — 1.   13£.     2.  7|.     3.  26.     4.  24.     5.   15  A 

6.  71.       7.   7A.       8.  8J.       9.   13|f.        10.   30.        11.   20&.        12.   18||. 

13.  21 A     14.  33  A-     15.  28f     16.  45. 

Page  235.    Article  11.  — 1.  A.     2.  |.    3.  £.    4.  i.     5.  £.     6.  f. 

7.  ft  »•  f  9-  *•  10-  *•  11  *•  12.  *•  13.  i-  14.  AV  15.  ft 
16.  ±. 

Page  235.    Article  13.-1.  A>  A,  if.      2.  ft  ft  A.      3. 

if-   *  ft  &,  &■   s-  i§>  H>  if-    6-  ft  ft>  ft-    7-  ft  A.  tV 

Page  236.  Article  14.-1.  ttfc  ^  AV  2.  A.  jfc  if-  3.  M 
ft  ft-     4.  AV,  Jfc,  -fc      5.  ft,  ft  &•      6.  ||i  «|,  HI-      7.  ft  f  J 

ft     »•  f t ft  s¥A  Hft 

Page  236.  Article  15.  — 1.  ft  2.  }.  3.  IjV  4.  1A-  5.  }f 
6.  1TV      7.  17V     8.  ft     9.  |f.      10.  lft      11.   I3V      12.   Itt- 

Page  237.  Article  16.  — 1.  2*.  2.  lft  3.  2AV  4.  2U 
5.  2¥V  6.  lj}.  7.  Iff.  8.  ltfj.  9.  175f.  10.  7*ft  11.  181f 
12.  56*. 

Page  238.  Article  17.  — 1.  A.  2.  i.  3.  A-  4.  A.  5.  If 
«    if.      7.  A-      8.  A      9.  if       10.  A.       11.  A-   ■   12-  it-      13-  0. 

14.  0.       15.  A- 

Page    238.     Article   18.  — 1.   3  A       2.   54.       3.    lft       4.    15U 
5.   10  A      6.  7A-      7.  4ft      8.   7ft      9.   21 A 
Page   238.     Article    19.  —  1.  A-       2-  h       3.   7^  yds.      4.  $5A- 

5.  $lft 

Page  239.     Article  20.  — 1.  3£.      2.  4f      3.  3£.      4.  5f.      5.  6$. 

6.  3f.      7.  3 A-      8.   If.      9.  27|.      10.   50|.      11.  69.      12.  36£. 
Page  239.     Article  21.  — 1.   16.      2.  16.      3.  30.      4.  15.      5.  6f 

6.  21.      7.   24.      8.  48.      9.   36. 

Page  240.  Article  23.  — 1.  |,  2.  ft  3.  A.  4.  If.  5.  2j. 
6.  if.  7.  f.  8.  if-  9-  3*.  10.  61.  11.  A  12-  ft  13-  A 
14.   15|.      15.   19|.      16.   f      17.  ft      18.  yft      19.  39TV      20.   75f 

Page   241.      Article    24.  — 1.   la.       2.   $A-       3-   $ft       4.   $f. 

5.  $A-      6.  $0.10f.      7.   A.      8.   59|m. 

Page  242.     Article  26.-1.  A       2.  A-      3.  A-      4.  A-     «    A- 

6.  A-  7.  A-  8.  A-  9-  if-  10.  3J.  11.  4A  12.  4A  13.  8X, 
14.  §A-  15.  6A-  16.  5A-  17.  9A-  18-  3T\.  19.  llf.  20.  9ft 
21.  3ff. 

Page  243.  Article  27.  — 1.  27.  2.  33$.  3.  28$.  4.  60.  5.  68f 
6.   113|.      7.    126.      8.   63.      9.   8A-       10.   2f       11.    13i       12.   5A- 


318  ANSWERS. 

Page  244.  Article  29—1.  H.  2.  li.  3.  U.  4.  1*.  5.  |. 
6.  J|.     7.    Ift.     8.    13.     9.   5§.     10.   3|.     11.   8§.     12.  21. 

Page  245.  Article  30.  — 1.  ft.  2.  ft.  3.  14  b.  4  ft.  5.  $5.40 
6.  99.  7.  17  p.  8.  38pkgs.  9.  $5.  10.  13§yds.  11.  8  jars.  12,  j-  of 
3  lbs.;  fibs.  13.  «•  !*•  90/.  15.  10^.  16.  1$  mi.  17.  35  qrs. 
18.  $3$.  19.  fift.;  7&  in.  20.  40?.  21.  l£  doz.  22.  18  vrs. 
23.  $1.20.  24.  2£  times.  25.  13£;  21f ;  |.  26.  f.  27.  68±  *. 
28.  82£  ft.      29.  8  prs.      30.  33£  da. 

Page  247.  Article  31.  — 1.  137^  yds.  2.  $5  ft.  3.  73 A.  4.  ft. 
5.  427fms.      6.  52|  oz.      7.  $58$.      8.  $194gJ.      9.  $128|.     10.  131^  a. 

11.  307T\90  bu.  12.  $3801.  13.  $3480.  14.  lOf  tons.  15.  $3A. 
16.  9}  lbs.  17.  4j.  18.  ft.  19.  H.  20.  60*.  21.  8  wks. ;  S118. 
22.  £  still  own,  $3000.  23.  $125,  36  times.  24.  44  yr. ;  18  yr. ;  15  yr. ; 
12  yr. ;  6  yr. ;   143  yr. 

Page  254.     Article  13.  —  1.  ft.     2.  yfa.     3.  ft.     4.  ft.     5.  J,. 

14.  18*fo.  15.  16&.  16.  rf5.  17.  90r^.  18.  60&.  19.  19£j|. 
2D.  180T^. 

Page  255.  Article  14.  —  1.  .375.  2.  30.75.  3.  .25.  4.  62.5. 
5.    .8.       6.    .075.       7.    .0625.       8.    .875.      9.    .26.      10.    .46§.       11.    .45. 

12.  33.33*.  13  .66$.  14.  .064.  15.  12.08.  16.  .41f.  17.  16.66f. 
18.  .0178f. 

Page  255.  Article  15—  1.  2.515.  2.  3150.098.  3.  233.4668. 
4.   15038.0359.     5.  234.93  yds.     6.   70.176.     7.  455.144366. 

Page    256.     Article   16.— 1.  104.39.        2.  22.0755.         3.  900.135. 

4.  .72.         5.   .8991.       6.   19.011.       7.  628.2616.        8.   .069993.         9.   .81. 

10.  83.11.      11.    105.3324. 

Page  257.     Article  18.  — 1.  .18142.    2.  .08316.    3.  1205.    4.  12.05. 

5.  3.1552.     6.   1869.6.     7.  246.048.     8.  24.6048.     9.  1150.56.     10.  11505.6. 

11.  .000081.     12.   .072. 

Page  258.     Article  21.  —  1.  230.  2.  2300.  3.  4.4.    4.  440. 

5.  257.4281  6.  2430.  7.  24.3.  8.  1000.  9.  86.137^.  10.  10,000. 
11.  .0046f|.      12.   1.561U.      13.  32,825.      14.   25,742.857f      15.  3.375§f. 

Page  258.  Article  22.  — 1.  8000.01353.  2.  182.15  bbls.  3.  .91375. 
4.  38.625  gals.  5.  $960.  6.  56.5  gals.  7.  626ft  A.  8.  $1,675. 
9.  .0078125.  10.  3.67644.  11.  $123.5.  12.  38.4375  yds.  13.  $29.2685. 
14.  1000  bottles.      15.  253.65. 

Page  261.  Article  25.  — 1.  $25,005.  2.  $9,011.  3.  $17.17. 
4.  $7,017.      5.   12.075.      6.  $111,011.      7.  $1001.001.      8.  2000.025. 

Page  262.     Article  26.  — 1.  34000  m.       2.  25,250  m.       3.  535  m. 

4.  980  m.  5.  24655  m.  6.  9125  m.  7.  672  m.  8.  100,750  m. 
9.  18,964  m.  10.  750  m.  11.375  m.  12.  1,600,620  m.  13.  13,145  m. 
14.  755.      15.  8625  m.      16.  46,024  m. 

Page  263.    Article  27.  —  1.  $12.     2.  $120.    3.  $290.18.    4.  $1.60. 

5.  1.20.      6.   2.50.      7.  $25. 

Page  263.  Article  28.  — 1.  $58.30.  2.  $4168.64.  3.  $55,025. 
4.   396.68.      5.  300.90. 

Page  264.  Article  30.  —  1.  $865,731.  2.  $0,505.  3.  20-dollar 
gold  piece  and  5-dol.  piece.  4.  $26,644.  5.  $4,125.  6.  Two  20-dol. 
gold  pieces.  7.  163.44  yds.  8.  $7080.48.  9.  70  lbs.  10.  356  da. 
11.  46  wks.      12    $0,375. 

Page  266.     Bills.    13.  $91.54.      14.  97.26.      15.  $103,215. 

Pagt  269.     Articles.  — 1.  561  pt.     2.  504  qt.     3.  790pt.     4.  60  pt. 

Page  269.  Article  6,  -  1.  12  bu.  3  pk.  1  pt. ;  5±  bu.  2.  10  bu.  2  pk. 
5  qt. ;  5  pk.  7  qt.»l  pt.      3.  3  bu.  3  pk.  5  qt. ;  5  pk.  3  qt.  1  pt. 


ANSWERS.  319 

Page  270.     Article   7.  — 1.    120  pt.  576  gi.        2.    559  gi.j   64  gi. 

3.  11  gal.  3  qt.;  5  gal.  3  qt.  1  pt.  4.  10  qt.  1  pt.  2  gi.;  3  gal.  2  gi. 
5.  804  gi.  ;  152  pt. 

Page  271.  Article  8.  — 1.  6000  lbs. ;  9600  oz.  2.  11977  oz. ; 
288000  oz.  3.  27  T.  1  cwt.  45  lbs. ;  230£  lbs.  4.  364  cwt.  25  lbs. ;  1  T. 
5.  11236  1b. 

Page  272.  Article  10.  — 1.  292  pkgs.  2.  $15.12.  3.  385  bu. 
3  pk.  1  qt.   4.  $35.   5.  17}  da. 

Page  272.  Article  11.  — 1.  198ft.;  258.5  ft.  2.  27072  in. ;  5760 
rd.  3.  1410  rd. ;  320760  in.  4.  158400  in. ;  3468  in. ;  1224  in. ;  4718.4  in. 

5.  3  mi.  9  rd.  3  yd.  2£  ft. ;  1  mi.  ;  10  mi.  40  rd. ;  4  mi. ;  9  mi.  7.  240  rd. 
8.  £  mi.   9.  1961  times.   10.  24  rd.  4  ft.   11.  93.5  ft.   12.  8  min. 

Page  274.  Article  14.  —  1.  38115  sq.  ft.  2.  2880  sq.  rds. 
3.  536.405  sq.  ft.  4.  4,014,489,600  sq.  in.  5.  30497  sq.  ft.  6.  9  A; 
27  A.   7.  18  sq.  yd.   8.  40  sq.  rd.   9.  I  sq.  mi.   10.  9  sq.  mi. 

Page  275.  Article  15.  — 1.  6  sq.ft.  2.  108  sq.  in. ;  120  sq.  in. 
3.  1080  sq.  in.   4.  180  sq.  ft.   5.  12  ft.   6.  1  A.  2  sq.  rd.   7.  $5664. 

Page  278.  Article  19. —1.  46656  cu.  in.;  31104  cu.  in.  2.  20736 
cu.  in.    3.  1687£  cu.  ft.    4.  2048  cu.  ft. ;  1312  cu.  ft.    5.  12  cu.  ft. 

6.  20  cu.  ft.   7.  432000  cu.  in.   8.  861264  cu.  in.   9.  9  cords;  50  cords. 

10.  120  cu.  ft.  11.  128  cu.  ft.  12.  155520  cu.  in.  13.  2700  cu.  ft. 
14.  1536  cu.  ft.  15.  2£  cords.  16.  $22.68.  17.  12  cu.  ft.  18.  $57,656  + 

Page  280.  Article  21.  — 1.  43200  sec. ;  7200  min.  2.  736800  sec. 
3.  41760  min.   4.  1  da.  ;  1  da.   5.  6  yrs. ;  9  yrs.  9  da.  8  hrs.  16  min. 

Page  281.  Article  23.  —  1.  75  bu.  3  pk.  4  qt.  2.  76  mi.  268  rd.  3  yd. 
3.  40  wk.  5  da.  11  hr.  24  min.  50  sec.   4.  69  gal.  3  qt.  1  pt. 

Page  281.  Article  24. —1.  11  gal.  3  gi.  2.  19  cwt.  98  lb.  11  oz. 
3.  10  wk.  2  da.  20  hr.  9  min.  5.  15  yr.  5  mo.  27  da. 

Page  282.  Article  25.  — 1.  450  mi.  276  rd.  4  yd.  2  ft.  3  in.  2.  69 
gal.  3  qt.   3.  49  T.  5  cwt.  1'6  lb.  8  oz.   4.  130  cu.  yds.  4  cu.  ft.  63  cu.  in. 

5.  84  sq.  yds.  1  sq.  ft.  142  sq.  in.   6.  57  yrs.  9  mos.   7.  58  bu.  2  pk. 

8.  110  A.  40  sq.  rd.   9.  38  yr.  2  mo. 

Page  283.  Article  26.  — 1.  8  bu.  1  pk.  7J  qts.   2.  5  gal.  If  pts. 

3.  1  cwt.  82  lb.  9  oz.  4.  4  hr.  36  min.  22  sec.  5.  2  cu.  yd.  26  cu.  ft. 
If  cu.  in.  6.  3  sq.  yd.  1  sq.  ft.  125£  sq.  in.  7.  5  rd.  4  yd.  10  in.  8.  12 
bottles,  2  pt.  rem.  9.  13  sacks. 

Page  284.  Article  27.-3.  156£  sq.  ft.  4.  140  sq.  rds.  5.  28&A. 

6.  3466|  sq.  yd.   7.  51 J  sq.  yd.   8.  51£  sq.  yds.   10.  196f  sq.  yd. 

11.  88f  sq.  yd.  12.  20  steps.  14.  57f  yd.  15.  51f  yd.  16.  8*  yd. 
17.  6.875  cords.  18.  40£  cords.  19.  1296  boxes.  20.  990  boards. 
21.  200  trees.   22.  225  loads. 

Page  290.   Article  3.-2.  24,32,36,  10.    3.  16,  24,  38f,  44|. 

4.  24.5,  56.7,  90.      5.  $82.03.      6.  $39,048,  $62.50.      7.   12  da.     8.  275  bu. 

9.  500  bu.  10.  $0.15125,  $0.15.  11.  $40.  12.  $30.  13.  12  absent ;  188 
present.     14.  100  A. 

Page  291.  Article  4.-2.  33£  %,  20%,  14f  %.  3.  ll£  %,  33£  %. 
4.  16£  %,  16|  %•  5-  7i%.  6.  41  %,  6  %,  20  %,  25  %.  7.  25  %  25  %. 
8.  33£  %.     9.   75  %.     10.    133£  %. 

Page  292.  Article  5.-2.  800,400,600.  3.  200,300,400.  4.  200, 
160,400.      5.  80,200,50.      6.  100,  10,16£.      7.  640.      8.  $944.      9.  $900. 

10.  $1500.  11.  $10.  12.  200  bu.  13.  150  A.  14.  $3000.  15.  $60. 
16.  5  ft.      17.  4  ft.      18.   160  rd. 

.Pages  293  and  294.  Article  3.-3.  $12,  $24.  4.  $10.  5.  $30. 
6.  $60.      7.   $30.      8.  $3.      9.  $18. 

Page  294.  Article  7.-2.  $48.15,  $56,175.  3.  $68.83£,  $110.13$. 
4.  $12,274,  $8,182$.     5.  $222,282.    6.  $243.11$.    7.$711.96f.    8.  $1337.66$. 


320  ANSWERS. 

Page  295.     Article  8.  — 1.   12,4,  4.      2.4,4.      3.36,12.  4.20%. 

5.   $6.     6.   50%.     7.   12.     8.   12^.     9.   33£  %.     10.  5  ft.  3.6  in.  11.   25  f. 

12.   75%.        13.  5%.      14.    10%.       15.  $1.37j.       16.  9T\  %.  17.   Sir,. 

18.   20%,  f.       19.   19^.       20.   30,400,300.       21.  10,100,200.  22.    l£ 

times,  150%.  23.  $7.00.  24.  150  ft.  25.  92.16  ft.  26.  72^,6* 
27.  $0.06.      28.   8yr.,  2  yr.      29.  3  yr.      30.   $10.^. 

Page  298. —  1.   5  bu.         2.   300*  57.6.         3.    $12,^.         4.    21   1.1.1s. 

5.  28  men.      6.  62£  da.      7.   $2.52. 

Page  299.  — 1.  it  yds.      2.  $£.      3.  3£  es.      4.  ^  lb.       5.  $  apples. 

6.  4  lamps — 40  f  rem.         7.    7  children.         8.    2|  boxes.         9.   4  vds. 

10.  720  books.     11.   6i  mo. 

Page  300.  — 1.  .645.  2.  11.072.  3.  4186.316.  4.  $4000.  5.  $187.50. 
6.   $34,167.     7.  1458.48.     8.   $16000.     9.   735.399t82Vt-      10-   1285.474^. 

Page  301. —  1.  54  children.  2.  240  tiles.  3.  1518|  bricks. 
4.  16  times.      5.   864  blocks.      6.   2066f£  gal.      7.   293^  loads. 

1.  Papering  and  Plastering. — 1.  \~\  sq.  yds.  2.  24j$  sq.  yd. ; 
83jf  sq.  yd.     3.  72j  sq.  yd.     5.  30£  rolls. 

Page  303. —  2.  16£ft.:  9^  ft.  3.  67^  ft.  4.  20*ft.  5.  266|  ft. 
6.   8jft. 

Page  304.  —  1.  $0.80.  2.  $0.60.  3.  $1.00.  4.  $1.50.  5.  12£  %. 
6.   40  %.      7.  20  %.      8.  25  %.      9.  $2*.       10.   91|  %. 

Page  305.  — 11.  20%  ;  16f%.  12.  $250;  $125;  $75;  $50.  13.  SI 25. 
14.    20  %.     15.    32  %  ;  44  %  ;  50  %.     16.    50%. 

Page  306.  — 1.  $960.  2.  $423.  3.  $99.45.  4.  $148.40.  5.  $61.20; 
$65.48. 

Page  307. —  6.  $41.25.    7.  $46.67.    8.  $73.50.    9.  $11.20.    10.  $2.07. 

11.  16cts.  12.  81  cts.  13.  $318.92.  14.  $20.  15.  $18.75.  16.  545. 
17.   $35.    18.    $61.43.     19.   $76.56.     20.  $156.80.     21.   $9.19.    22.    $58.84. 


541;]  24 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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